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Tytuł:
Application of Differential Transform Method to triple diffusion convective boundary layer flow of Casson nanofluid over a horizontal plate
Autorzy:
Asha, S. K.
Mali, Gayitri
Powiązania:
https://bibliotekanauki.pl/articles/1839391.pdf
Data publikacji:
2021
Wydawca:
Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
Tematy:
Differential Transformation Method
Casson nanofluid
horizontal plate
Opis:
In this paper, triple diffusive convective boundary layer flow of Casson nanofluid along a horizontal plate is investigated theoretically when nonlinear thermal radiation impact is considered. The suitable similarity transformations is utilized for the reduction of a set of basic governing nonlinear PDEs into nonlinear non-dimensional ODEs. By using differential Transform Method (DTM) with the help of symbolic software Mathematica, the reduced nonlinear non-dimensional ordinary differential equations are solved. Further, velocity, temperature, solutal and nanofluid concentration profiles are presented graphically and studied in details by using various physical parameters.
Źródło:
World Scientific News; 2021, 162; 161-178
2392-2192
Pojawia się w:
World Scientific News
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Szacowanie niepewności przy kalibracji ogniw wzorcowych w Centralnym Wojskowym Ośrodku Metrologii
Uncertainty estimation of standard cells calibration at the Primary Standards Laboratory
Autorzy:
Woźniak, E.
Powiązania:
https://bibliotekanauki.pl/articles/209171.pdf
Data publikacji:
2008
Wydawca:
Wojskowa Akademia Techniczna im. Jarosława Dąbrowskiego
Tematy:
ogniwo wzorcowe
metoda różnicowa
kalibracja
niepewność
standard cell
differential method
calibration
uncertainty
Opis:
W artykule zaprezentowano procedurę szacowania niepewności wyznaczania wartości siły elektromotorycznej ogniw wzorcowych nietermostatowanych metodą różnicową w laboratorium elektrycznym Centralnego Wojskowego Ośrodka Metrologii. Prezentowany przykład dotyczy szczególnego przypadku szacowania niepewności, w którym składniki niepewności oszacowane metodami statystycznymi (typu A) mają znaczne udziały w złożonej niepewności standardowej.
The procedure for uncertainty evaluation of standard cells calibration at the Primary Standards Laboratory is presented in the article. The example concerns a particular case where uncertainty contributions, evaluated statistically (type A), are quite meaningful in the uncertainty budget.
Źródło:
Biuletyn Wojskowej Akademii Technicznej; 2008, 57, 2; 339-353
1234-5865
Pojawia się w:
Biuletyn Wojskowej Akademii Technicznej
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A review: differential transform method for semi-analytical solution of differential equations
Autorzy:
Rashidi, M. M.
Rabiei, F.
Naser Nia, S.
Abbasbandy, S.
Powiązania:
https://bibliotekanauki.pl/articles/265637.pdf
Data publikacji:
2020
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
metoda transformacji różniczkowej
równania różniczkowe
metoda półanalityczna
differential transform method
differential transform - Pad'e approximation
semi-analytical method
differential equations
fuzzy differential transformation method
gS-differentiability
Opis:
In this article, the semi-analytical method known as the Differential Transform Method (DTM) for solving different types of differential equations is reviewed. First, basic definitions and formulas of DTM and Differential Transform-Padé approximation (DTM-Padé), which are used to increase the convergence and accuracy of DTM approximations, are discussed. Then both techniques of DTM and DTM-Padé, which have been successfully applied to partial differential equations, as well as the application of these methods in fluid mechanic and heat transfer are presented. In addition, the extension of DTM for integral differential equations and the fuzzy differential transformation method (FDTM) for fuzzy problems are discussed.
Źródło:
International Journal of Applied Mechanics and Engineering; 2020, 25, 2; 122-129
1734-4492
2353-9003
Pojawia się w:
International Journal of Applied Mechanics and Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Application of the differential transform method to the free vibration analysis of functionally graded timoshenko beams
Autorzy:
Özdemir, Ö.
Powiązania:
https://bibliotekanauki.pl/articles/281244.pdf
Data publikacji:
2016
Wydawca:
Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
Tematy:
differential transform method
functionally graded beam
Timoshenko beam
Opis:
In this study, free vibration characteristics of a functionally graded Timoshenko beam that undergoes flapwise bending vibration is analysed. The energy expressions are derived by introducing several explanotary figures and tables. Applying Hamilton’s principle to the energy expressions, governing differential equations of motion and boundary conditions are obtained. In the solution part, the equations of motion, including the parameters for rotary inertia, shear deformation, power law index parameter and slenderness ratio are solved using an efficient mathematical technique, called the differential transform method (DTM). Natural frequencies are calculated and effects of several parameters are investigated.
Źródło:
Journal of Theoretical and Applied Mechanics; 2016, 54, 4; 1205-1217
1429-2955
Pojawia się w:
Journal of Theoretical and Applied Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Effect of hydrogen peroxide and lead(II) nitrate on gold cyanide leaching of Malaysian mesothermal deposit gold ore
Autorzy:
Baharun, Norlia
Ling, Ong Pek
Ardani, Mohammad Rezaei
Ariffin, Kamar Shah
Powiązania:
https://bibliotekanauki.pl/articles/1845218.pdf
Data publikacji:
2020
Wydawca:
Politechnika Wrocławska. Oficyna Wydawnicza Politechniki Wrocławskiej
Tematy:
gold cyanidation
mesothermal lode gold
statistical analysis
design of experiment
Van’t Hoff differential method
Opis:
The gold extraction from Malaysian mesothermal lode gold ore through the cyanidation method was performed. The effect of hydrogen peroxide (H2O2) and lead nitrate Pb(NO3)2 were investigated on the percentage of gold recovery. The statistical analysis method using a response surface design-central composite design was applied to find the optimum condition for gold extraction. The studied parameters were NaCN concentration (300-500 ppm), H2O2 concentration (205-410 ppm), and Pb(NO3)2 concentration (50-150 ppm). It was found that increasing the amount of NaCN and H2O2 as well as decreasing the amount of Pb(NO3)2 in the studied range, increased the gold recovery. The analysis of variance suggested the linear model for the gold extraction with the optimum condition at 467.3 ppm NaCN, 94.96 ppm Pb(NO3)2, and 340 ppm H2O2. The gold extracted from the ore at the optimum condition was 88.97% as compared to 62.02% from conventional cyanidation. The characterization study of the gold ore indicated that the finely gold particles interlocked in the aluminosilicate phase (grain size of ~10.0 μm). The Van’t Hoff differential method justified that the cyanidation was of second order with a specific reaction rate of 0.0501/hour.
Źródło:
Physicochemical Problems of Mineral Processing; 2020, 56, 5; 905-918
1643-1049
2084-4735
Pojawia się w:
Physicochemical Problems of Mineral Processing
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Differential Transform Method for the Kinetic Analysis of Thermal Inactivation of Enzyme as Applied in Biotechnology
Autorzy:
Adeleye, O. A.
Sobamowo, M. G.
Akinnukawe, B. I.
Powiązania:
https://bibliotekanauki.pl/articles/1031487.pdf
Data publikacji:
2020
Wydawca:
Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
Tematy:
Analytical solution
Differential transformation method
Enzyme
Kinetic analysis
Thermal inactivation
Opis:
In this work, approximate analytical solution is developed using differential transformation method for finding the molar concentration of the native and denatured enzyme in terms of second-order rate constant. Also, the obtained solutions are used to study the kinetics of thermal inactivation of enzyme as applied in biotechnology. The analytical solution was validated with numerical solution using fourth- order Runge-Kutta. Good agreement was established between the numerical and approximated analytical solutions.
Źródło:
World Scientific News; 2020, 142; 135-149
2392-2192
Pojawia się w:
World Scientific News
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Three-dimensional thermal buckling analysis of functionally graded cylindrical panels using differential quadrature method (DQM)
Autorzy:
Ahmadi, S. A.
Pourshahsavari, H.
Powiązania:
https://bibliotekanauki.pl/articles/949112.pdf
Data publikacji:
2016
Wydawca:
Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
Tematy:
thermal buckling
curved panel
functionally graded material
differential quadrature method
Opis:
Thermal buckling analysis of functionally graded cylindrical panels subjected to various conditions is discussed in this paper. Buckling governing equations are solved using the differential quadrature method. It is assumed that the mechanical properties of the panel are graded through thickness according to a power function of the thickness variable. The panel is assumed to be under the action of three types of thermal loading including uniform temperature rise and variable temperature rise in the axial and radial direction. In the present study, the effects of power law index, panel angle, different thermal load conditions and geometric parameters on the buckling behavior of functionally graded curved panels are studied. The results obtained through the present method are compared to the finite element solutions and the reported results in the literature. A desirable compatibility is concluded.
Źródło:
Journal of Theoretical and Applied Mechanics; 2016, 54, 1; 135-147
1429-2955
Pojawia się w:
Journal of Theoretical and Applied Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Free vibration analysis of isotropic rectangular plates on Winkler foundation using differential transform method
Autorzy:
Kumar, Y.
Powiązania:
https://bibliotekanauki.pl/articles/265747.pdf
Data publikacji:
2013
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
metoda transformacji
izotropia
differential transform method
isotropic
rectangular
Winkler foundation
Opis:
A differential transform method (DTM) is used to analyze free transverse vibrations of isotropic rectangular plates resting on a Winkler foundation. Two opposite edges of the plates are assumed to be simply supported. This semi-numerical-analytical technique converts the governing differential equation and boundary conditions into algebraic equations. Characteristic equations are obtained for three combinations of clamped, simply supported and free edge conditions on the other two edges, keeping one of them to be simply supported. Numerical results show the robustness and fast convergence of the method. Correctness of the results is shown by comparing with those obtained using other methods.
Źródło:
International Journal of Applied Mechanics and Engineering; 2013, 18, 2; 589-597
1734-4492
2353-9003
Pojawia się w:
International Journal of Applied Mechanics and Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A comparative study of differential transformation and homotopy perturbation methods for transient combustion analysis for iron micro-particles in a gaseous oxidizing medium
Autorzy:
Yinusa, A. A.
Sobamowo, M. G.
Powiązania:
https://bibliotekanauki.pl/articles/1046539.pdf
Data publikacji:
2019
Wydawca:
Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
Tematy:
Differential transformation method
Homotopy perturbation method
Iron particle combustion
Temperature distribution
Thermal radiation
Opis:
In this paper, a comparative study of differential transformation and homotopy perturbation methods for transient combustion analysis of iron micro-particles in a gaseous oxidizing medium is presented. Also, parametric studies are carried out to properly understand the reaction of the process and the associated burning time. Thermal radiation effect from the external surface of burning particle and variation of iron particle density with temperature are considered. The solutions obtained by DTM and HPM are compared with those of the fourth order Runge-Kutta numerical method. Results show that DTM has more accurate results between the two approximate analytical methods considered. Also, results show that by increasing the heat realized parameter, combustion temperature increased and it faster reaches to its constant value. It is envisaged that the present study will create tremendous insight into means of properly managing combustible micro particles exiting factories and production process organization.
Źródło:
World Scientific News; 2019, 138, 2; 93-112
2392-2192
Pojawia się w:
World Scientific News
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Analytical investigation of heat transfer in a moving convective porous fin with temperature dependent thermal conductivity and internal heat generation
Autorzy:
Sobamowo, M. G.
Waheed, M. A.
Powiązania:
https://bibliotekanauki.pl/articles/1031762.pdf
Data publikacji:
2020
Wydawca:
Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
Tematy:
Convective fin
Differential transformation method
Moving fin
Porous Fin
Thermal analysis
Opis:
In the present study, thermal performance of a rectangular moving porous fin with temperature dependent thermal conductivity and internal heat generation are analyzed the differential transformation method. The developed approximate analytical solutions are used to investigate the effects of thermal –geometric and thermo-physical fin parameters such as the Peclet number, thermal conductivity parameter, convection parameter, porosity parameter, Internal heat generation parameter on the dimensionless temperature distribution and heat transfer rate are discussed. From the results, it is found that increase in porosity and convective parameters, the rate of heat transfer from the fin increases and consequently improve the efficiency of the fin. Also, the values of the temperature distribution in the fin increases as the Peclet number increases. However, as thermal conductivity and the internal heat generation increase, the rate of heat transfer from the fin decreases. The analytical solution is found to be in good agreement with the direct numerical solution.
Źródło:
World Scientific News; 2020, 150; 1-21
2392-2192
Pojawia się w:
World Scientific News
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the Analysis of Jump and Bifurcation Phenomena in a Forced Vibration of Geometrical Nonlinear Cantilever Beam: Application of Differential Transformation Method
Autorzy:
Sobamowo, M. G.
Yinusa, A. A.
Adeleye, O. A.
Oyelade, A. O.
Sadiq, O. M.
Powiązania:
https://bibliotekanauki.pl/articles/1031911.pdf
Data publikacji:
2020
Wydawca:
Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
Tematy:
Bifurcation Phenomenon
Differential transformation method
Jump phenomenon
Nonlinear vibration
Phase plane
Opis:
One of the classical features exhibited in nonlinear dynamics of engineering systems is the jump phenomenon, which is the discontinuous change in the steady state response of a system as a parameter is slowly varied. Such phenomenon is characterized by large amplitude dynamic responses of systems to small amplitude disturbances. It is established that this phenomenon cannot be described by the standard asymptotic and perturbation methods because they are limited to the study of small amplitude responses to small disturbances. Therefore, this paper presents the application of differential transformation method-Padé approximant to the solution of jump and bifurcation phenomena for a geometrical nonlinear cantilever beam subjected to a harmonic excitation. The accuracy and validity of the analytical solutions obtained by the differential transformation method are shown through a comparison of the results of the analytical solution with the corresponding results of the numerical solution obtained by fourth-order Runge-Kutta method and also with the results in a past study using harmonic balancing method. With the aid of the differential transformation method-Padé approximant, the effects of the nonlinear parameters in the model equation on the dynamic response of the beam are investigated. Also, the sensitivity of the beam to the external excitation amplitude is analyzed. In the distributed forced vibration, the jump phenomenon appeared in the response amplitude by variation of the excitation frequency while in the resonance frequency, the beat phenomenon with harmonic motion is seen for low level of excitation amplitude. At a certain frequency, the jump and bifurcation phenomena are seen in the curves of responses versus excitation amplitude. Additionally, the plots of the phase plane and time history of the system response are shown. It is established that the differential transformation method is a very useful mathematical tool for dealing with the nonlinear problems.
Źródło:
World Scientific News; 2020, 140; 26-58
2392-2192
Pojawia się w:
World Scientific News
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Analysis of axially loaded tapered beams with general end restraints on two-parameter foundation
Autorzy:
Taha, M. H.
Nassar, M.
Powiązania:
https://bibliotekanauki.pl/articles/280518.pdf
Data publikacji:
2014
Wydawca:
Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
Tematy:
tapered beams
elastic end restraints
two-parameter foundation
differential quadrature method
Opis:
The stability and free vibration of axially-loaded tapered beams with elastic end restraints resting on two-parameter foundations are studied using the differential quadrature method (DQM). The governing differential equation is discretized at sampling points, and then the boundary conditions due to elastic end restraints are implemented and substituted into the governing differential equation yielding a system of homogeneous algebraic equations. The equivalent two-parameter eigenvalue problem is obtained and solved for critical loads in the static case and for natural frequencies in the dynamic case. The obtained solutions are found compatible with those obtained from other techniques. The influences of different parameters on the critical loads and natural frequencies are investigated.
Źródło:
Journal of Theoretical and Applied Mechanics; 2014, 52, 1; 215-225
1429-2955
Pojawia się w:
Journal of Theoretical and Applied Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Thermal and fluid analysis on effects of a nanofluid outside of a stretching cylinder with magnetic field using the Differential Quadrature Method
Autorzy:
Ghasemi, S. E.
Hatami, M.
Salarian, A.
Domairry, G.
Powiązania:
https://bibliotekanauki.pl/articles/281394.pdf
Data publikacji:
2016
Wydawca:
Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
Tematy:
nanofluids
Differential Quadrature Method (DQM)
heat transfer
streching cylinder
magnetic field
Opis:
In this paper, magnetohydrodynamic flow (MHD) of a nonofluid over a stretching cylinder is investigated numerically. The Differential Quadrature Method (DQM) is applied for solving the governing equations. The influence of relevant parameters such as the magnetic parameter, the solid volume fraction of nanoparticles and the type of nanofluid on the flow, heat transfer, Nusselt number and skin friction coefficient is discussed. Also, comparison with the published results is presented. The results show that the Nusselt number increases with growth in the volume fraction coefficient and Reynolds number but decreases with the magnetic parameter.
Źródło:
Journal of Theoretical and Applied Mechanics; 2016, 54, 2; 517-528
1429-2955
Pojawia się w:
Journal of Theoretical and Applied Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Methods based on the differential quadrature in vibration analysis of plates
Metody oparte na kwadraturach różniczkowych w zastosowaniu do drgań płyt
Autorzy:
Krowiak, A.
Powiązania:
https://bibliotekanauki.pl/articles/281788.pdf
Data publikacji:
2008
Wydawca:
Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
Tematy:
kwadratury różniczkowe
drgania własne
differential quadrature method
spline interpolation
free vibration
Opis:
The paper deals with the methods based on the differential quadrature and their application to the free vibration analysis of plates. The spline-based differential quadrature Method (SDQM) is presented as an alternative to known methods based on the interpolation polynomial (PDQM). The SDQM uses a polynomial piecewise function to approximate the wanted solution of a governing equation. The way of determining the spline functions as well as the way of computing weighting coefficients for the method are presented in the paper. Then the SDQM is applied to determine natural frequencies of plates. The influence of the spline degree, number of nodes and grid point distribution on the accuracy, convergence and stability is investigated in an example. All results are compared with values obtained by the conventional differential quadrature method (PDQM).
Praca dotyczy metod opartych na kwadraturach różniczkowych i ich aplikacji do zagadnienia drgań własnych płyt. W pracy, jako alternatywę do znanych metod kwadratur różniczkowych, opartych na wielomianie interpolacyjnym (PDQM), przedstawiono metodę bazującą na funkcjach sklejanych (SDQM). W SDQM poszukiwane rozwiązanie przybliżane jest funkcją wielomianową, przedziałami zmienną. W pracy przedstawiono sposób wyznaczenia takiej funkcji interpolacyjnej, jak również sposób obliczenia współczynników wagowych, używanych w metodzie kwadratur różniczkowych. Następnie SDQM użyto do wyznaczenia częstości drgań własnych płyt, gdzie analizowano wpływ stopnia wielomianu, liczby węzłów i ich rozmieszczenia na zbieżność, dokładność i stabilność metody. Otrzymane rezultaty porównano z wynikami uzyskanymi przy pomocy konwencjonalnej metody kwadratur różniczkowych (PDQM).
Źródło:
Journal of Theoretical and Applied Mechanics; 2008, 46, 1; 123-139
1429-2955
Pojawia się w:
Journal of Theoretical and Applied Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the Efficiency of Differential Transformation Method to the Solutions of Large Amplitude Nonlinear Oscillation Systems
Autorzy:
Sobamowo, M. G.
Yinusa, A. A.
Adeleye, O. A.
Alozie, S. I.
Salawu, S. A.
Salami, M. O.
Powiązania:
https://bibliotekanauki.pl/articles/1031949.pdf
Data publikacji:
2020
Wydawca:
Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
Tematy:
Analytical solution
Differential transformation method
Large amplitude
Oscillation system
Strong nonlinearity
Opis:
In this work, the efficiency of differential transformation method to the solutions of large amplitude nonlinear oscillatory systems is further established. Two cases of oscillation systems, nonlinear plane pendulum and pendulum in a rotating plane are considered. Without any linearization, discretization or series expansion of the sine and cosine of the angular displacement in the nonlinear models of the systems, the differential transformation method with Padé approximant is used to provide analytical solutions to the nonlinear problems. Also, the increased predictive power and the high level of accuracy of the differential transformation method over the previous methods are presented. The extreme accuracy and validity of the analytical solutions obtained by the differential transformation method are shown through comparison of the results of the solution with the corresponding numerical solutions obtained by fourth-fifth-order Runge-Kutta method. Also, with the aid of the analytical solutions, parametric studies were carried to study the impacts of the model parameters on the dynamic behavior of the large-amplitude nonlinear oscillation system. The method avoids any numerical complexity and it is very simple, suitable and useful as a mathematical tool for dealing the nonlinear problems.
Źródło:
World Scientific News; 2020, 139, 1; 1-60
2392-2192
Pojawia się w:
World Scientific News
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Application of the multi-step differential transform method to solve a fractional human T-cell lymphotropic virus I (HTLV-I) infection of CD4+ T-cells
Autorzy:
Zurigat, M.
Ababneh, M.
Powiązania:
https://bibliotekanauki.pl/articles/357712.pdf
Data publikacji:
2015
Wydawca:
Politechnika Rzeszowska im. Ignacego Łukasiewicza. Oficyna Wydawnicza
Tematy:
fractional differential equations
differential transform method
HTLV-I
numerical solution
równanie różniczkowe cząstkowe
obliczenia numeryczne
Opis:
Human T-cell Lymphotropic Virus I (HTLV-I) infection of $CD4^{+}$ T-Cells is one of the causes of health problems and continues to be one of the significant health challenges. In this article, a multi-step differential transform method is implemented to give approximate solutions of fractional modle of HTLV-I infection of $CD4^{+}$ T-cells. Numerical results are compared to those obtained by the fourth-order Runge-Kutta method in the case of intger-order derivatives. The suggested method is efficient as the Runge-Kutta method. Some plots are presented to show the reliability and simplicity of the method.
Źródło:
Journal of Mathematics and Applications; 2015, 38; 171-180
1733-6775
2300-9926
Pojawia się w:
Journal of Mathematics and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Machine Learning Methods in Algorithmic Trading Strategy Optimization – Design and Time Efficiency
Autorzy:
Ryś, Przemysław
Ślepaczuk, Robert
Powiązania:
https://bibliotekanauki.pl/articles/1356900.pdf
Data publikacji:
2019-08-09
Wydawca:
Uniwersytet Warszawski. Wydział Nauk Ekonomicznych
Tematy:
Algorithmic trading
investment strategy
machine learning
optimization
differential evolutionary method
cross-validation
overfitting
Opis:
The main aim of this paper was to formulate and analyse the machine learning methods, fitted to the strategy parameters optimization specificity. The most important problems are the sensitivity of a strategy performance to little parameter changes and numerous local extrema distributed over the solution space in an irregular way. The methods were designed for the purpose of significant shortening of the computation time, without a substantial loss of strategy quality. The efficiency of methods was compared for three different pairs of assets in case of moving averages crossover system. The problem was presented for three sets of two assets’ portfolios. In the first case, a strategy was trading on the SPX and DAX index futures; in the second, on the AAPL and MSFT stocks; and finally, in the third case, on the HGF and CBF commodities futures. The methods operated on the in-sample data, containing 16 years of daily prices between 1998 and 2013 and was validated on the out-of-sample period between 2014 and 2017. The major hypothesis verified in this paper is that machine learning methods select strategies with evaluation criterion near the highest one, but in significantly lower execution time than the brute force method (Exhaustive Search).
Źródło:
Central European Economic Journal; 2018, 5, 52; 206 - 229
2543-6821
Pojawia się w:
Central European Economic Journal
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Effects of Internal Heat Generation on the Thermal Stability of a Porous Fin
Autorzy:
Sobamowo, M. G.
Jayesimi, L. O.
Waheed, M. A.
Powiązania:
https://bibliotekanauki.pl/articles/1031875.pdf
Data publikacji:
2020
Wydawca:
Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
Tematy:
Differential Transformation Method
Porous Fin
Temperature-Dependent Internal Heat Generation
Thermal analysis
Thermal performance
Opis:
In this study, the effects of internal heat generation on thermal stability of porous fin is theoretical investigated using differential transform method. The parametric studies reveal increase in the internal heat generation leads to increase in the value or the range of the thermal stability of the fin. The internal heat generation can be used to control the thermal instability in the fin. Also, as the porosity parameter increase, the rate of heat transfer from the base of the fin and consequently improve the efficiency of the fin increase. However, a high value or an excessive internal heat generation results in an undesirable situation where some of the heat energy cannot escape to the sink and instead ends up flowing into the prime surface and the fin tends to store heat rather than dissipating it. This scenario defeats the prime purpose of the cooling fin. Therefore, the operational parameters must be carefully selected to ensure that the fin retains its primary purpose of removing heat from the primary surface.
Źródło:
World Scientific News; 2020, 149; 110-127
2392-2192
Pojawia się w:
World Scientific News
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Nonlinear Analysis of a Large-Amplitude Forced Harmonic Oscillation System using Differential Transformation Method-Padé Approximant Technique
Autorzy:
Sobamowo, M. G.
Yinusa, A. A.
Oyekeye, M. O.
Folorunsho, S. S.
Powiązania:
https://bibliotekanauki.pl/articles/1031931.pdf
Data publikacji:
2020
Wydawca:
Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
Tematy:
Large amplitude; Oscillation system; Strong nonlinearity; Forced vibration; Differential transformation method-Padé approximant techniques
Opis:
This work presents the nonlinear analysis of forced harmonic oscillation system using differential transformation method-Padé approximant techniques. Without any series expansion of the included sine and cosine of the angular displacement in the nonlinear model of the system, an improved analytical solution of the dynamic model is presented. The high level of accuracy and validity of the analytical solutions obtained by the differential transformation method are shown through comparison of the results of the solution with the corresponding numerical solutions obtained by fourth-fifth-order Runge-Kutta method, homotopy perturbation method and energy balance methods. Also, with the aid of the analytical solutions, parametric studies are carried to study the impacts of the model parameters on the dynamic behavior of the large-amplitude nonlinear oscillation system. The method avoids any numerical complexity and it is very simple, suitable and useful as a mathematical tool for dealing the nonlinear problems.
Źródło:
World Scientific News; 2020, 140; 139-155
2392-2192
Pojawia się w:
World Scientific News
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A numerical approximation of 2D coupled burgers’ equation using modified cubic trigonometric B-spline differential quadrature method
Autorzy:
Kapoor, Mamta
Joshi, Varun
Powiązania:
https://bibliotekanauki.pl/articles/2174173.pdf
Data publikacji:
2022
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
równanie Burgersa
aerodynamika
fala uderzeniowa
differential quadrature method
Runge-Kutta 43 scheme
trigonometric B-spline
Opis:
In the present paper, trigonometric B-spline DQM is applied to get the approximated solution of coupled 2D non-linear Burgers’ equation. This technique, named modified cubic trigonometric B-spline DQM, has been used to obtain accurate and effective numerical approximations of the above-mentioned partial differential equation. For checking the compatibility of results, different types of test examples are discussed. A comparison is done between 2L and L∞ error norms with the previous, present results and with the exact solution. The resultant set of ODEs has been solved by employing the SSP RK 43 method. It is observed that the obtained results are improved compared to the previous numerical results in the literature.
Źródło:
International Journal of Applied Mechanics and Engineering; 2022, 27, 3; 79--102
1734-4492
2353-9003
Pojawia się w:
International Journal of Applied Mechanics and Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Integral equation of the Volterra type: an application to a firm-sponsored off-the-job training
Autorzy:
Ekhosuehi, Virtue U
Powiązania:
https://bibliotekanauki.pl/articles/748734.pdf
Data publikacji:
2016
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
firm
production function
Volterra integral equation
firm, differential transform method, production function, Volterra integral equatio
Opis:
W artykule poszukuje  sie funkcji produkcji pojedynczego produktu w przedsiebiorstwie finansującym szkolenia ze środków uzyskanych ze sprzedazy tego produktu.  Funkcja produkcji ma zalozona forme  równania całkowego Volterry a kryterium optymalizacji jest krótkoterminowa  maksymalizacja zysku, w którym praca jest jedynym czynnikiem produkcji.  W badaniu wykorzystano funkcję Cobba-Douglasa z ustalona iloscia kapitału. Wyniki wskazują, że otrzymana funkcja produkcji firmy jest funkcją analityczną, a wymagana część zysku potrzebna do sfinansowania szkolenia leży w przedziale z określoną górną granicą.
This paper is concerned with deriving, using the Volterra integral equation, a production function for a single product firm financing off-the-job training from its revenue from output. The short-run scenario where labour is the only variable factor of production is studied within the ambit of the law of diminishing returns and the condition for profit-maximization. The study utilizes the Cobb-Douglas production function wherein capital is fixed as a theoretical underpinning. The results indicate that the production function of the firm is a transcendental function and that the proportion of output required to finance the training lies within an interval with a definite upper bound.
Źródło:
Mathematica Applicanda; 2016, 44, 2
1730-2668
2299-4009
Pojawia się w:
Mathematica Applicanda
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Uncertainty of determining the energy equivalent speed (EES) of a vehicle collision by the experimental and analytical method
Niepewność w określeniu prędkości EES zderzenia samochodów wyznaczanej metodą eksperymentalno-analityczną
Autorzy:
Sztwiertnia, K.
Guzek, M.
Powiązania:
https://bibliotekanauki.pl/articles/1363357.pdf
Data publikacji:
2017
Wydawca:
Sieć Badawcza Łukasiewicz. Przemysłowy Instytut Motoryzacji
Tematy:
deformation work
energy methods
accident reconstruction
total differential method
uncertainly of ESS
praca deformacji
metody energetyczne
rekonstrukcja wypadków
metoda różniczki zupełnej
niepewność EES
Opis:
One of the basic ways to estimate vehicle speeds at the reconstruction of vehicle collisions is the use of methods generally referred to as “energy methods”, where a relation between the “energy equivalent speed” (EES) and the size of permanent vehicle deformation is described. There are several mathematical models used in practice to describe such a relation. Usually, a linear relation between the deformation size (depth) and the energy consumed to cause the deformation (“deformation work”) is assumed. In contrast, the deformation itself and the deformation energy are described in various ways. In consequence, different EES values may be obtained from the calculations, depending on the model used. In the accident reconstruction practice, an increasingly important role is played by the uncertainty and reliability of the analysis results obtained. This article is dedicated to the uncertainty of estimation of the energy equivalent speed (EES). The uncertainty calculation results obtained with the use of one of the typical methods of determining it, i.e. the total differential method, have been presented. The calculations were carried out for five analytical models used to determine the deformation work, based on the deformation size, for several real cases of post-impact vehicle deformation. The calculation results have been presented in the form of tables and graphs, thanks to which comparisons between both the EES values and the values of their absolute and relative uncertainty could be made. The whole analysis has ended with conclusions concerning the values obtained; they may be a source of information on the uncertainty in determining the EES parameter depending on the computation model used.
Jednym z podstawowych sposobów stosowanych przy rekonstrukcji zderzeń samochodów, wykorzystywanym w celu oszacowania ich prędkości, jest grupa tzw. metod energetycznych. W metodach tych opisuje się związek między prędkością równoważną energii EES (z ang. energy equivalent speed), a rozmiarem trwałego odkształcenia pojazdu. Istnieje kilka praktycznie wykorzystywanych modeli matematycznych opisujących ten związek. Zazwyczaj zakładają one liniową zależność między wspomnianym rozmiarem (głębokością) deformacji, a energią zużytą na jej powstanie (tzw. pracą deformacji). W różny sposób natomiast opisywana jest sama deformacja oraz energia deformacji. W zależności od zastosowanego modelu możemy otrzymać inne wartości poszukiwanej prędkości EES. W praktyce rekonstrukcji wypadków coraz istotniejszą rolę odgrywa niepewność i wiarygodność otrzymanych wyników. Przedmiotem artykułu jest niepewność oszacowania prędkości równoważnej energii EES. W pracy zostały przedstawione wyniki obliczeń otrzymane przy użyciu jednej z typowych metod jej określania – metody różniczki zupełnej. Obliczenia zostały wykonane dla pięciu modeli analitycznych wyznaczania pracy deformacji, na podstawie jej rozmiaru, dla kilku rzeczywistych odkształceń pozderzeniowych pojazdów. Wyniki przedstawiono w postaci tabelarycznej oraz wykresów, umożliwiających porównanie zarówno wartości parametru EES, jak i wyznaczonych dla niego niepewności bezwzględnych oraz względnych. Całość została podsumowana wnioskami odnoszącymi się do otrzymanych wartości. Mogą one być źródłem informacji na temat niepewności w wyznaczaniu prędkości EES w zależności od zastosowanego modelu obliczeniowego.
Źródło:
Archiwum Motoryzacji; 2017, 76, 2; 123-136
1234-754X
2084-476X
Pojawia się w:
Archiwum Motoryzacji
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Investigation of a Jeffery-Hamel flow between two rectangular inclined smooth walls using the differential Transform Method
Autorzy:
Patel, N. D.
Meher, R.
Powiązania:
https://bibliotekanauki.pl/articles/122393.pdf
Data publikacji:
2018
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
Differential Transform Method
Jeffery-Hamel flow
higher order non-linear ordinary differential equation
metoda transformacji różnicowej
DTM
przepływ Jeffery-Hamela
nieliniowe równanie różniczkowe
Opis:
In this article, the Differential Transform Method (DTM) is applied to derive a semi-analytic solution for the non-linear MHD (Magneto Hydro Dynamics) Jeffery-Hamel flow between rectangular inclined smooth planes. A non-linear ordinary differential equation of order four is obtained from Navier-Stokes equations using similar transformation. A comparison between DTM, PM (Perturbation Method) and numerical solution is shown here to validate the obtained results with its convergence analysis for different values of m and a Reynolds number in divergent channels.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2018, 17, 4; 47-57
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Nonlinear mechanics of a compliant beam system undergoing large curvature deformation
Autorzy:
Akano, Theddeus Tochukwu
Olayiwola, Patrick Shola
Powiązania:
https://bibliotekanauki.pl/articles/1845010.pdf
Data publikacji:
2020
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
compliant beam
differential transformation method
large deformation
nonlinear equation
mechanics
metoda transformacji różniczkowej
duże odkształcenie
równanie nieliniowe
mechanika
Opis:
A compliant beam subjected to large deformation is governed by a multifaceted nonlinear differential equation. In the context of theoretical mechanics, solution for such equations plays an important role. Since it is hard to find closed-form solutions for this nonlinear problem and attempt at direct solution results in linearising the model. This paper investigates the aforementioned problem via the multi-step differential transformation method (MsDTM), which is well-known approximate analytical solutions. The nonlinear governing equation is established based on a large radius of curvature that gives rise to curvature-moment nonlinearity. Based on established boundary conditions, solutions are sort to address the free vibration and static response of the deforming flexible beam. The geometrically linear and nonlinear theory approaches are related. The efficacy of the MsDTM is verified by a couple of physically related parameters for this investigation. The findings demonstrate that this approach is highly efficient and easy to determine the solution of such problems. In new engineering subjects, it is forecast that MsDTM will find wide use.
Źródło:
Archive of Mechanical Engineering; 2020, LXVII, 4; 471-489
0004-0738
Pojawia się w:
Archive of Mechanical Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Mixed convective fully developed flow in a vertical channel in the presence of thermal radiation and viscous dissipation
Autorzy:
Prasad, K. V.
Mallikarjun, P.
Vaidya, H.
Powiązania:
https://bibliotekanauki.pl/articles/265697.pdf
Data publikacji:
2017
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
mixed convection
thermal radiation
viscous dissipation
Differential Transform Method (DTM)
Perturbation Method (PM)
konwekcja mieszana
promieniowanie cieplne
metoda transformacji różnicowej
metoda zakłóceń
Opis:
The effect of thermal radiation and viscous dissipation on a combined free and forced convective flow in a vertical channel is investigated for a fully developed flow regime. Boussinesq and Roseseland approximations are considered in the modeling of the conduction radiation heat transfer with thermal boundary conditions (isothermal-thermal, isoflux-thermal, and isothermal-flux). The coupled nonlinear governing equations are also solved analytically using the Differential Transform Method (DTM) and regular perturbation method (PM). The results are analyzed graphically for various governing parameters such as the mixed convection parameter, radiation parameter, Brinkman number and perturbation parameter for equal and different wall temperatures. It is found that the viscous dissipation enhances the flow reversal in the case of a downward flow while it counters the flow in the case of an upward flow. A comparison of the Differential Transform Method (DTM) and regular perturbation method (PM) methods shows the versatility of the Differential Transform Method (DTM). The skin friction and the wall temperature gradient are presented for different values of the physical parameters and the salient features are analyzed.
Źródło:
International Journal of Applied Mechanics and Engineering; 2017, 22, 1; 123-144
1734-4492
2353-9003
Pojawia się w:
International Journal of Applied Mechanics and Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Problem with integral condition for evolution equation
Autorzy:
Kalenyuk, P. I.
Kuduk, G.
Kohut, I. V.
Nytrebych, Z. M.
Powiązania:
https://bibliotekanauki.pl/articles/357782.pdf
Data publikacji:
2015
Wydawca:
Politechnika Rzeszowska im. Ignacego Łukasiewicza. Oficyna Wydawnicza
Tematy:
analiza funkcjonalna
przestrzeń Banacha
równania ewolucyjne
równania różniczkowe
functional analysis
Banach space
evolution equation
integral conditions
differential-symbol method
Opis:
We propose a method of solving the problem with non-homogeneous integral condition for homogeneous evolution equation with abstract operator in a linear space H. For right-hand side of the integral condition which belongs to the special subspace H ⊆ L, in which the vectors are represented using Stieltjes integrals over a certain measure, the solution of the problem is represented in the form of Stieltjes integral over the same measure.
Źródło:
Journal of Mathematics and Applications; 2015, 38; 71-76
1733-6775
2300-9926
Pojawia się w:
Journal of Mathematics and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The Generalized Differential Transform Method for solution of a free vibration linear differential equation with fractional derivative damping
Autorzy:
Das, Deepanjan
Powiązania:
https://bibliotekanauki.pl/articles/122961.pdf
Data publikacji:
2019
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
fractional differential equations
Caputo fractional derivative
generalized
differential transform method
analytic solution
ułamkowe równania różniczkowe
ułamkowa pochodna Caputo
metoda transformacji różnicowej
rozwiązanie analityczne
ułamkowe równanie różniczkowe
Opis:
In the present paper, the Generalized Differential Transform Method (GDTM) is used for obtaining the approximate analytic solutions of a free vibration linear differential equation of a single-degree-of-freedom (SDOF) system with fractional derivative damping. The fractional derivatives are described in the Caputo sense.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2019, 18, 2; 19-29
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A new modification of the reduced differential transform method for nonlinear fractional partial differential equations
Autorzy:
Khalouta, Ali
Kadem, Abdelouahab
Powiązania:
https://bibliotekanauki.pl/articles/1839758.pdf
Data publikacji:
2020
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
nonlinear fractional partial differential equations
Caputo fractional derivative
Shehu transform method
reduced differential transform method
approximate analytical solution
nieliniowe równania różniczkowe cząstkowe ułamkowe
pochodna ułamkowa Caputo
metoda transformacji Shehu
metoda transformacji różnicowej
Opis:
The objective of this study is to present a new modification of the reduced differential transform method (MRDTM) to find an approximate analytical solution of a certain class of nonlinear fractional partial differential equations in particular, nonlinear time-fractional wave-like equations with variable coefficients. This method is a combination of two different methods: the Shehu transform method and the reduced differential transform method. The advantage of the MRDTM is to find the solution without discretization, linearization or restrictive assumptions. Three different examples are presented to demonstrate the applicability and effectiveness of the MRDTM. The numerical results show that the proposed modification is very effective and simple for solving nonlinear fractional partial differential equations.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2020, 19, 3; 45-58
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A study on magneto hydrodynamics Jeffery-Hamel flow with heat transfer problem in Eyring-Powell fluid using differential transform method
Autorzy:
Meher, Ramakanta
Patel, N. D.
Powiązania:
https://bibliotekanauki.pl/articles/122591.pdf
Data publikacji:
2019
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
Differential Transform Method
Jeffery-Hamel flow
Eyring-Powell fluid
heat transfer
metoda transformacji różnicowej
przepływ Jeffery-Hamela
przenikanie ciepła
płyn Eyringa-Powella
Opis:
In this paper, we study and analyse the variations of velocity profiles for different values of the Reynolds number, Eckert number, Prandtl number and Hartmann number in the Magneto Hydrodynamics Jeffery-Hamel flow with heat transfer in Eyring-Powell fluid in both divergent and convergent channels. The Differential Transform Method (DTM) is used to obtain an analytical solution of the Jeffery Hamel flow problem and to determine the velocity profiles of the fluid flow. Finally, the efficiency of DTM has been shown, and the results have been validated by comparing the obtained results with the numerical results (fourth order RK method) in both convergent and divergent channels.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2019, 18, 3; 57-68
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Some averaging results for ordinary differential inclusions
Autorzy:
Bourada, Amel
Guen, Rahma
Lakrib, Mustapha
Yadi, Karim
Powiązania:
https://bibliotekanauki.pl/articles/729511.pdf
Data publikacji:
2015
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
ordinary differential inclusions
averaging method
Opis:
We consider ordinary differential inclusions and we state and discuss some averaging results for these inclusions. Our results are proved under weaker conditions than the results in the literature.
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2015, 35, 1; 47-63
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Metoda Frobeniusa, czyli o rozwiązywaniu pewnej klasy równań różniczkowych
Autorzy:
Wiśniewski, Damian
Żyjewski, Krzysztof
Powiązania:
https://bibliotekanauki.pl/articles/1789275.pdf
Data publikacji:
2017-07-05
Wydawca:
Uniwersytet Pedagogiczny im. Komisji Edukacji Narodowej w Krakowie
Tematy:
Frobenius method
series solutions
differential equations
Opis:
The article is a comprehensive research paper which provides theoreticalas well as practical aspects of the Ferdinand George Frobenius method.This method is based on seeking infinite series solutions for certainclass of differential equations. It is a generalization of the power series methodand allows us to solve the differential equations at least near somesingular points.
Źródło:
Annales Universitatis Paedagogicae Cracoviensis. Studia ad Didacticam Mathematicae Pertinentia; 2016, 8; 139-158
2080-9751
2450-341X
Pojawia się w:
Annales Universitatis Paedagogicae Cracoviensis. Studia ad Didacticam Mathematicae Pertinentia
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the Chaplygin method for the Darboux problem
Autorzy:
Jaruszewska-Walczak, Danuta
Powiązania:
https://bibliotekanauki.pl/articles/745871.pdf
Data publikacji:
2007
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
functional differential equation
Newton method
analytical approximations
Opis:
In the paper we deal with the Darboux problem for hyperbolic functional differential equations. We give the sufficient conditions for the existence of the sequence \(\{z^{(m)}\}\) such that if \(\tilde{z}\) is a classical solution of the original problem then \(\{z^{(m)}\}\) is uniformly convergent to z\(\tilde{z}\). The convergence that we get is of the Newton type.
Źródło:
Commentationes Mathematicae; 2007, 47, 1
0373-8299
Pojawia się w:
Commentationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Impulsive differential equations with initial data difference
Autorzy:
Skóra, Lidia
Powiązania:
https://bibliotekanauki.pl/articles/745364.pdf
Data publikacji:
2011
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
impulsive differential equation
impulsive differential inequalities
existence
monotone iterative method
extremal solutions
Opis:
In this paper, we present some results on impulsive differential inequalities and equations with initial and impulsive data difference.
Źródło:
Commentationes Mathematicae; 2011, 51, 1
0373-8299
Pojawia się w:
Commentationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Note on the stability of first order linear differential equations
Autorzy:
Bojor, F.
Powiązania:
https://bibliotekanauki.pl/articles/255364.pdf
Data publikacji:
2012
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
fixed point method
differential equation
Hyers-Ulam stability
Opis:
In this paper, we will prove the generalized Hyers-Ulam stability of the linear differential equation of the form y'(x)+f (x) y(x)+g(x) = 0 under some additional conditions.
Źródło:
Opuscula Mathematica; 2012, 32, 1; 67-74
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Existence of minimal and maximal solutions to RL fractional integro-differential initial value problems
Autorzy:
Denton, Z.
Ramirez, J. D.
Powiązania:
https://bibliotekanauki.pl/articles/255901.pdf
Data publikacji:
2017
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
Riemann Liouville derivative
integro-differential equation
monotone method
Opis:
In this work we investigate integro-differential initial value problems with Riemann Liouville fractional derivatives where the forcing function is a sum of an increasing function and a decreasing function. We will apply the method of lower and upper solutions and develop two monotone iterative techniques by constructing two sequences that converge uniformly and monotonically to minimal and maximal solutions. In the first theorem we will construct two natural sequences and in the second theorem we will construct two intertwined sequences. Finally, we illustrate our results with an example.
Źródło:
Opuscula Mathematica; 2017, 37, 5; 705-724
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Convergences Analysis from the Solution Function of the Riccati Fractional Differential Equation by Using Modified Homotopy Perturbation Method
Autorzy:
Sevira, Nurazizah M.
Rusyaman, Endang
Firdaniza, Firdaniza
Subiyanto, Subiyanto
Supian, Sudradjat
Powiązania:
https://bibliotekanauki.pl/articles/1059423.pdf
Data publikacji:
2019
Wydawca:
Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
Tematy:
Convergent
Differential Equation
Fractional
Modified Homotopy Perturbation Method
Riccati
Opis:
A Fractional differential equation is an equation that contains derivatives with an order of fractional numbers. Same with natural number order differential equations, this type of equation is divided into linear and nonlinear fractional differential equations. One of the equations that include nonlinear fractional differential equation is Riccati fractional differential equation (RFDE). Various methods have been applied to find solutions for fractional differential equations Riccati, one of them is the Modified Homotopy Perturbation Method (MHPM) which is a modification of the Homotopy Perturbation Method by Zaid Odibat and Shaher Momani. In this study, the MHPM was used to find solutions for fractional differential equations Riccati, which were then used to analyze the convergence of the function sequences of the solution. The result shows us that the order sequence of Riccati fractional differential equation which converges to a number causes the solution function sequence of Riccati fractional differential equation will converge to the function of the solution of Riccati fractional differential equation with the order of this number.
Źródło:
World Scientific News; 2019, 128, 2; 71-87
2392-2192
Pojawia się w:
World Scientific News
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Quasilinearization method for finite systems of nonlinear RL fractional differential equations
Autorzy:
Denton, Zachary
Ramirez, Juan Diego
Powiązania:
https://bibliotekanauki.pl/articles/1397341.pdf
Data publikacji:
2021
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
fractional differential systems
lower and upper solutions
quasilinearization method
Opis:
In this paper the quasilinearization method is extended to finite systems of Riemann-Liouville fractional differential equations of order 0 < q < 1. Existence and comparison results of the linear Riemann-Liouville fractional differential systems are recalled and modified where necessary. Using upper and lower solutions, sequences are constructed that are monotonic such that the weighted sequences converge uniformly and quadratically to the unique solution of the system. A numerical example illustrating the main result is given.
Źródło:
Opuscula Mathematica; 2020, 40, 6; 667-683
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Purification of Hexabenzylhexaazaisowurtzitane
Autorzy:
Gołofit, T.
Maksimowski, P.
Powiązania:
https://bibliotekanauki.pl/articles/358605.pdf
Data publikacji:
2016
Wydawca:
Sieć Badawcza Łukasiewicz - Instytut Przemysłu Organicznego
Tematy:
HBIW
CL-20
purification
differential scanning calorimetry
cryometric method
Opis:
Hexabenzylhexaazaisowurtzitane (HBIW) is produced by a condensation reaction of benzylamine with glyoxal in suitable organic solvents in the presence of protonic acid catalysts. Impurities have to be removed prior to the subsequent stages of the synthesis of CL-20. The effectiveness of HBIW purification by recrystallization from a variety of solvents has been studied here. This method was compared with a novel approach suggested for HBIW purification that consists of prolonged heating of the crude product in boiling methanol. This new purification method allows the product to be prepared in satisfactory purity, it is simple and easily performed on a large-scale.
Źródło:
Central European Journal of Energetic Materials; 2016, 13, 4; 1038-1050
1733-7178
Pojawia się w:
Central European Journal of Energetic Materials
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Identification of an Electrically Driven Manipulator Using the Differential Filters – Input Error Method
Autorzy:
Cedro, L.
Powiązania:
https://bibliotekanauki.pl/articles/387029.pdf
Data publikacji:
2012
Wydawca:
Politechnika Białostocka. Oficyna Wydawnicza Politechniki Białostockiej
Tematy:
filtry różniczkujące
identyfikacja
differential filters
identification
input error method
Opis:
The paper presents an example of solving the parameter identification problem in case of robot with three degrees of freedom has been presented. The identification has been performed with the use of elaborated differential filters. The applied identification method does not require differential equations solving but only determining the appropriate derivatives. Identification method and its generalizations using the object inverse model require information on time derivatives of the input and output signals. The required derivative order depends on the order of differential equations describing the object.
Źródło:
Acta Mechanica et Automatica; 2012, 6, 2; 23-27
1898-4088
2300-5319
Pojawia się w:
Acta Mechanica et Automatica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Calculation of distribution of temperature in three-dimensional solid changing its shape during the process
Autorzy:
Bożek, B.
Mączka, C.
Powiązania:
https://bibliotekanauki.pl/articles/255226.pdf
Data publikacji:
2005
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
parabolic partial differential equations
non-stationary distribution of heat
finite element method
Galerkin method
Opis:
The present paper suplements and continues [2]. Galerkin method for the Fourier-Kirchoff equation in the case when Omega(t) - equation domain, dependending on time t, is constructed. For special case Omega(t) rcup R2 the computer program for above method is written. Binaries and sources of this program are available on http://wms.mat.agh.edu.pl/~bozek.
Źródło:
Opuscula Mathematica; 2005, 25, 2; 169-179
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Issledovanie dinamiki ustrojjstva dlja narezanija rezby
The study of the dynamics of a device for screw thread turning
Autorzy:
Gevko, B.
Djachun, A.
Marchuk, N.
Powiązania:
https://bibliotekanauki.pl/articles/76522.pdf
Data publikacji:
2016
Wydawca:
Komisja Motoryzacji i Energetyki Rolnictwa
Tematy:
operation
maintenance
mechanical engineering
thread connection
nonlinear differential equation
numerical method
Runge-Kutta method
Źródło:
Motrol. Motoryzacja i Energetyka Rolnictwa; 2016, 18, 1
1730-8658
Pojawia się w:
Motrol. Motoryzacja i Energetyka Rolnictwa
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Series Solution of Nonlinear Ordinary Differential Equations Using Single Laplace Transform Method in Mathematical Physics
Autorzy:
Mbagwu, JP. C.
Madububa, B. I.
Nwamba, J. I.
Powiązania:
https://bibliotekanauki.pl/articles/1193352.pdf
Data publikacji:
2021
Wydawca:
Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
Tematy:
Adomian polynomials
Single Laplace transform method
nonlinear ordinary differential equations
Opis:
In this paper, a novel technique is created to enable the extension of the single Laplace transform method (SLTM) to solve nonlinear ordinary differential equations (ODEs) is presented. The main parts of the recommended technique are the Adomian polynomials. By developing several theorems, which include the Laplace transformation of nonlinear expressions, the Adomian polynomials are made possible. Several famous nonlinear equations including the Blasius equation, the Poisson Boltzmann equation, and numerous extra problems relating nonlinearities of many types such as exponential and sinusoidal are resolved for description. As it was revealed in the specified equations, and problems, our technique is conceptually and computationally simple. Some nonlinear examples are taken from the literature for checking the validation and convergence of the proposed technique. The suggested method is methodical, precise, then restricted to integration.
Źródło:
World Scientific News; 2021, 154; 152-174
2392-2192
Pojawia się w:
World Scientific News
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Discretization of the stationary distribution of heat in the non-homogeneous body
Autorzy:
Bożek, B.
Powiązania:
https://bibliotekanauki.pl/articles/2049973.pdf
Data publikacji:
2004
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
elliptic partial differential equations
stationary distribution of heat
discretization method
Opis:
We give a short survey on the theory of the mixed boundary-value problem for the stationary Fourier equation in a non-homogeneous medium defined on any Lipschitz domain $\Omega \rcup \mathbb{R}^{n} (n \ge 2)$. The compatibility condition for the thermal flux has been established by the standard procedure of integration the divergence.
Źródło:
Opuscula Mathematica; 2004, 24, 1; 19-33
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On boundary value problems of second order differential inclusions
Autorzy:
Dhage, Bapur
Powiązania:
https://bibliotekanauki.pl/articles/729619.pdf
Data publikacji:
2004
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
differential inclusion
method of upper and lower solutions
existence theorem
Opis:
This paper presents sufficient conditions for the existence of solutions to boundary-value problems of second order multi-valued differential inclusions. The existence of extremal solutions is also obtained under certain monotonicity conditions.
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2004, 24, 1; 73-96
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The method of upper and lower solutions for perturbed nth order differential inclusions
Autorzy:
Dhage, Bupurao
Petruşel, Adrian
Powiązania:
https://bibliotekanauki.pl/articles/729580.pdf
Data publikacji:
2006
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
differential inclusion
method of upper and lower solutions
existence theorem
Opis:
In this paper, an existence theorem for nth order perturbed differential inclusion is proved under the mixed Lipschitz and Carathéodory conditions. The existence of extremal solutions is also obtained under certain monotonicity conditions on the multi-functions involved in the inclusion. Our results extend the existence results of Dhage et al. [7,8] and Agarwal et al. [1].
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2006, 26, 1; 57-76
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Forma osi gibkojj neszhimaemojj polosy pri ee tolkanii po naklonnojj sherokhovatojj ploskosti s postojannojj skorostju
Form of axis of flexible incompressible bar at its pushing on rough ramp with permanent speed
Autorzy:
Pylypaka, S.
Nesvidomin, A.
Zaharova, T.
Powiązania:
https://bibliotekanauki.pl/articles/78098.pdf
Data publikacji:
2013
Wydawca:
Komisja Motoryzacji i Energetyki Rolnictwa
Tematy:
differential equation
motion
friction
movement speed
slope angle
numerical method
Opis:
Worked out differential equations of the motion of flexible incompressible bar on a rough ramp at its pushing with permanent speed. The special cases of the motion are considered without friction, at the different angles of slope of plane, at the different corners of entry of bar on a plane. The form of axis of bar for the considered cases was found by the numeral methods of integration.
Źródło:
Motrol. Motoryzacja i Energetyka Rolnictwa; 2013, 15, 4
1730-8658
Pojawia się w:
Motrol. Motoryzacja i Energetyka Rolnictwa
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Linear differential equations of second, third, and fourth order
Autorzy:
Hernández-Galeana, A.
López-Bonilla, J.
López-Vázquez, R.
Vidal-Beltrán, S.
Powiązania:
https://bibliotekanauki.pl/articles/1167198.pdf
Data publikacji:
2018
Wydawca:
Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
Tematy:
Abel-Liouville-Ostrogradski identity
Euler-Lagrange method
Linear differential equation
Opis:
We study the linear differential equations of second, third, and fourth order, accepting to know solutions of the corresponding homogeneous equation, then we show how to obtain one more solution for the homogeneous case and a particular solution for the original equation.
Źródło:
World Scientific News; 2018, 105; 225-232
2392-2192
Pojawia się w:
World Scientific News
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Differential difference inequalities related to parabolic functional differential equations
Autorzy:
Netka, M.
Powiązania:
https://bibliotekanauki.pl/articles/255915.pdf
Data publikacji:
2010
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
parabolic functional differential equations
method of lines
stability and convergence
Opis:
Initial boundary value problems for nonlinear parabolic functional differential equations are transformed by discretization in space variables into systems of ordinary functional differential equations. A comparison theorem for differential difference inequalities is proved. Sufficient conditions for the convergence of the method of lines is given. Nonlinear estimates of the Perron type for given operators with respect to functional variables are used. Results obtained in the paper can be applied to differential integral problems and to equations with deviated variables.
Źródło:
Opuscula Mathematica; 2010, 30, 1; 95-115
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Sampling, Maintenance and Pathotype Identification of Synchytrium Endobioticum (Schilb.) Perc.
Autorzy:
Przetakiewicz, Jarosław
Powiązania:
https://bibliotekanauki.pl/articles/2199701.pdf
Data publikacji:
2017-12-20
Wydawca:
Instytut Hodowli i Aklimatyzacji Roślin
Tematy:
potato wart agent
differential cultivars
Glynne-Lemmerzahl method
winter sporangia
Opis:
Plant Breeding and Acclimatization Institute – National Research Institute (IHAR-PIB) is responsible for pathotype identification of Synchytrium endobioticum isolates collecting from Poland. Pathogenicity tests are carried out using the Glynne-Lemmerzahl method, according to EPPO Standard PM 7/28. Pathotypes are defined based on their reaction to a range of well-characterized differential cultivars of potato. Assessment of one isolate of the fungus requires more than 20 differential cultivars. All pathotypes of S. endobioticum from Polish reference collection are multiplied and maintained (fresh warts) on tubers of extremely susceptible cultivars continuously. For all references pathotypes and isolates of S. endobioticum, the compost with winter sporangia are prepared for long-term of maintenance.
Źródło:
Plant Breeding and Seed Science; 2017, 76; 29-36
1429-3862
2083-599X
Pojawia się w:
Plant Breeding and Seed Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Fusion of differential analysis of volumetric strain method (dilatometric thermoporometry) and mercury intrusion porosimetry method for pore space characterization in carbonate rocks
Połączenie metody różnicowej analizy odkształceń oraz metody porozymetrii rtęciowej do określenia charakterystyki przestrzeni porowej w skałach węglanowych
Autorzy:
Skowera, Karol
Powiązania:
https://bibliotekanauki.pl/articles/27314907.pdf
Data publikacji:
2023
Wydawca:
Politechnika Świętokrzyska w Kielcach. Wydawnictwo PŚw
Tematy:
differential analysis of volumetric strain method
mercury intrusion porosimetry
carbonate rocks
pore space
różnicowa analiza odkształceń
porozymetria rtęciowa
skały węglanowe
przestrzeń porowa
Opis:
Many characteristics of capillary-porous materials, including limestones and dolomites, depend on the structure of the pore space of a given material, so the article attempts to accurately determine the geometric characteristics of pores and their ability to transport water. Much information on the pore structure of carbonate rocks can be obtained from literature studies. There is a lack of information on the use of full hysteresis dilatometric thermoporometry methods for this purpose, as well as the fusion of differential analysis of volumetric strain (DAVS) results with mercury intrusion porosimetry (MIP) results. The subject of the research presented in this article is the analysis of pore structure in carbonate rocks using the method of differential analysis of volumetric strain and mercury intrusion porosimetry. Based on the measurements made, the pore size, pore volume, content of empty pores and pores containing water incapable of phase transformation were analyzed. The geometry of mesopores of rock samples examined by differential analysis of volumetric strain and mercury intrusion porosimetry was compared. A fusion of the distribution of mesopores from the DAVS study with a part of the distribution of meso- and macropores obtained by the MIP study was performer.
Wiele cech materiałów kapilarno-porowatych, w tym wapieni i dolomitów, zależy od struktury przestrzeni porowej danego materiału, dlatego w artykule podjęto próbę dokładnego określenia cech geometrycznych porów i ich zdolności do transportu wody. Wiele informacji na temat struktury porów skał węglanowych można uzyskać ze studiów literaturowych. Brakuje informacji na temat wykorzystania w tym celu metod termoporometrii dylatometrycznej z pełną histerezą, a także połączenia wyników różnicowej analizy odkształceń (DAVS) z wynikami porozymetrii rtęciowej (MIP). Przedmiotem badań przedstawionych w niniejszym artykule jest analiza struktury porów w skałach węglanowych z wykorzystaniem metody różnicowej analizy odkształceń i porozymetrii rtęciowej. Na podstawie przeprowadzonych pomiarów przeanalizowano wielkość porów, objętość porów, zawartość porów pustych oraz porów zawierających wodę niezdolną do przemiany fazowej. Porównano geometrię mezoporów próbek skalnych badanych metodą różnicowej analizy odkształceń i porozymetrii rtęciowej. Wykonano fuzję rozkładu mezoporów z badania DAVS z częścią rozkładu mezo- i makroporów uzyskanych w badaniu MIP.
Źródło:
Structure and Environment; 2023, 15, 2; 90--98
2081-1500
Pojawia się w:
Structure and Environment
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The Lipschitz Picard successive step method in hydrodynamic lubrication problem
Autorzy:
Wierzcholski, K.
Powiązania:
https://bibliotekanauki.pl/articles/247949.pdf
Data publikacji:
2012
Wydawca:
Instytut Techniczny Wojsk Lotniczych
Tematy:
Unified Pickard method
approximation of solutions
system of partial differential equations
Opis:
The paper shows the successive steps of approximation of Picard unification for the solution of the non-isothermal fluid flow in thin layer including inertia forces and apparent viscosities described by the non-linear dependences. In this paper is presented a unified semi analytical method of solution of the asymmetrical, laminar, steady and unsteady, non-Newtonian lubrication problem flow between two non-rotational in general, convex, differentiable and movable surfaces when the time t depended gap between mentioned surfaces has quite an arbitrary geometry. The presented considerations relate not only to the rotational cooperating surfaces but also to the arbitrary non-rotational surfaces in general. The parallel and longitudinal intersections of mentioned surfaces are curvilinear and non-monotone in general. We consider the non-Newtonian lubricant for non-linear constitutive equations taking into account Reiner Rivlin power law relationship as well Rivlin-Ericksen formula for viscoelastic fluids. The non-Newtonian properties create non-linear dependencies between strain and stress. Moreover, the dynamic viscosity or apparent dynamic viscosity of numerous lubricant liquids with various additions often decreases along with shear rate increasing during motion. Dynamic viscosity of lubricant fluids inside very thin micro and nano boundary layers depends on Young’s modulus of the cell of surface body being in contact with the fluid.
Źródło:
Journal of KONES; 2012, 19, 1; 483-490
1231-4005
2354-0133
Pojawia się w:
Journal of KONES
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Existence of solutions and monotone iterative method for infinite systems of parabolic differential-functional equations
Autorzy:
Brzychczy, Stanisław
Powiązania:
https://bibliotekanauki.pl/articles/1293995.pdf
Data publikacji:
1999
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
method of lower and upper functions
infinite systems of parabolic differential-functional equations
monotone iterative method
Opis:
We consider the Fourier first boundary value problem for an infinite system of weakly coupled nonlinear differential-functional equations. To prove the existence and uniqueness of solution, we apply a monotone iterative method using J. Szarski's results on differential-functional inequalities and a comparison theorem for infinite systems.
Źródło:
Annales Polonici Mathematici; 1999, 72, 1; 15-24
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Analysis of three-phases matrix reactance frequency converter with two pulsations of control signal
Autorzy:
Korotyeyev, I.Ye.
Zięba, B.
Powiązania:
https://bibliotekanauki.pl/articles/141295.pdf
Data publikacji:
2012
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
rozszerzenie równań różniczkowych
metoda Galerkina
matrix-reactance frequency converter
non-stationary periodic differential
Galerkin's method
extension of differential equations
Opis:
This paper presents a method of calculation of steady-state processes in threephases matrix-reactance frequency converters (MRFC's), in which voltages and currents are transformed by control signals with two pulsations. A solution of nonstationary differentia equations with periodic coefficients that describe this system is obtained by using Galerkin's method and an extension of equations of one variable of time to equations of two variables of time. The results of calculations are presented in an example of three-phases MRFC with buck-boost topology and compared with a numerical metod embedded in the program Mathematica.
Źródło:
Archives of Electrical Engineering; 2012, 61, 3; 359-371
1427-4221
2300-2506
Pojawia się w:
Archives of Electrical Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Boundary integral solution for a class of fourth-order two-point boundary value problems
Autorzy:
Al-Gahtani, H. J.
Powiązania:
https://bibliotekanauki.pl/articles/122949.pdf
Data publikacji:
2016
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
boundary integral method
fourth-order differential equation
nonlinear ordinary differential equations
nieliniowe równania różniczkowe zwyczajne
równanie różniczkowe czwartego rzędu
Opis:
In this paper, a boundary integral method is proposed for the solution of a class of fourth-order two-boundary value problems described by the equation yiv+P(x, y, y’, y’’, y’’’) = 0, x ∈ ( 0,L), where P is a polynomial function of its arguments. The differential equation is cast in an integral form and the weighted residual technique is used to generate the corresponding boundary integral equations. The boundary integral equations are then, solved by expressing the dependent variable, y, in terms of a power series. The proposed method is tested through four examples to show the applicability of the method to solve a wide range of fourth-order differential equations including the nonlinear ones.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2016, 15, 3; 5-13
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Monotone method for Riemann-Liouville multi-order fractional differential systems
Autorzy:
Denton, Z.
Powiązania:
https://bibliotekanauki.pl/articles/254754.pdf
Data publikacji:
2016
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
fractional differential systems
multi-order systems
lower and upper solutions
monotone method
Opis:
In this paper we develop the monotone method for nonlinear multi-order N-systems of Riemann-Liouville fractional differential equations. That is, a hybrid system of nonlinear equations of orders qi where 0 < qi < 1. In the development of this method we recall any needed existence results along with any necessary changes. Through the method's development we construct a generalized multi-order Mittag-Leffler function that fulfills exponential-like properties for multi-order systems. Further we prove a comparison result paramount for the discussion of fractional multi-order inequalities that utilizes lower and upper solutions of the system. The monotone method is then developed via the construction of sequences of linear systems based on the upper and lower solutions, and are used to approximate the solution of the original nonlinear multi-order system.
Źródło:
Opuscula Mathematica; 2016, 36, 2; 189-206
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Estimates of solutions for parabolic differential and difference functional equations and applications
Autorzy:
Sapa, L.
Powiązania:
https://bibliotekanauki.pl/articles/254895.pdf
Data publikacji:
2012
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
parabolic differential and discrete functional equations
estimate of solution
implicit difference method
Opis:
The theorems on the estimates of solutions for nonlinear second-order partial differential functional equations of parabolic type with Dirichlet's condition and for suitable implicit finite difference functional schemes are proved. The proofs are based on the comparison technique. The convergent and stable difference method is considered without the assumption of the global generalized Perron condition posed on the functional variable but with the local one only. It is a consequence of our estimates theorems. In particular, these results cover quasi-linear equations. However, such equations are also treated separately. The functional dependence is of the Volterra type.
Źródło:
Opuscula Mathematica; 2012, 32, 3; 529-549
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Model reduction techniques for linear constant coefficient port-Hamiltonian differential-algebraic systems
Autorzy:
Hauschild, Sarah-Alexa
Marheineke, Nicole
Mehrmann, Volker
Powiązania:
https://bibliotekanauki.pl/articles/970123.pdf
Data publikacji:
2019
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
structure-preserving model reduction
index reduction
port-Hamiltonian differential-algebraicsystem
moment matching
effort constraint method
flow constraint method
Opis:
The aim of this paper is to combine model order reduction for differential-algebraic equations with port-Hamiltonian structure preservation. For this, we extend two classes of model reduction techniques (reduction of the Dirac structure and moment matching) to handle port-Hamiltonian differential-algebraic equations. The performance of the methods is investigated for benchmark examples, originating from semi-discretized flow problems and mechanical multibody systems.
Źródło:
Control and Cybernetics; 2019, 48, 1; 125-152
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Nonlinear dynamic analysis of viscoelastic membranes described with fractional differential models
Analiza nieliniowej dynamiki lepko-sprężystych powłok opisanych modelem o pochodnej ułamkowej
Autorzy:
Katsikadelis, J. T.
Powiązania:
https://bibliotekanauki.pl/articles/280344.pdf
Data publikacji:
2012
Wydawca:
Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
Tematy:
viscoelastic membranes
nonlinear vibrations
nonlinear fractional differential equations
analog equation method
boundary elements
Opis:
The dynamic response of an initially flat viscoelastic membrane is investigated. The viscoelastic model is described with fractional order derivatives. The membrane is subjected to surface transverse and inplane dynamic loads. The governing equations are three coupled second order nonlinear partial FDEs (fractional differential equations) of hyperbolic type in terms of the displacement components. These equations are solved using the BEM for fractional partial differential equations developed recently by Katsikadelis. Without excluding other viscoelastic models, the herein employed material is the Kelvin-Voigt model with a fractional order derivative. Numerical examples are presented which not only demonstrate the efficiency of the solution procedure, but also give a better insight into this complicated but very interesting response of structural viscoelastic membranes. It is worth noting that in case of resonance, phenomena similar to those of the Duffing equation are observed.
W pracy przedstawiono analizę dynamiki płaskiej powłoki lepko-sprężystej po wstępnym ugięciu. Reologiczny model materiału powłoki opisano równaniem o pochodnych ułamkowych. Powłokę poddano płaskiemu, poprzecznemu obciążeniu zewnętrznemu. Zagadnienie dynamiki ujęto układem trzech sprzężonych nieliniowych równań różniczkowych typu hiperbolicznego o pochodnych ułamkowych. Równania rozwiązano metodą elementów brzegowych (BEM) sformułowaną przez autora właśnie dla układów opisanych pochodnymi ułamkowymi. W prezentowanej pracy założono, że powłoka wykonana jest z lepko-sprężystego materiału Kelvina-Voigta o pochodnej ułamkowej, choć samo sformułowanie BEM nie wyklucza możliwości analizy innych modeli reologicznych. Przedstawiono kilka przykładów symulacji numerycznych pokazujących efektywność zastosowanej metody rozwiązywania oraz dających lepszy obraz interesującej, lecz skomplikowanej dynamiki lepko-sprężystych powłok. Warto również podkreślić, że w warunkach rezonansowych odnotowano zjawiska podobne do obserwowanych w układzie Duffinga.
Źródło:
Journal of Theoretical and Applied Mechanics; 2012, 50, 3; 743-753
1429-2955
Pojawia się w:
Journal of Theoretical and Applied Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Coupled lateral-torsional vibrations of a symmetric rotor
Autorzy:
Chiliński, B.
Pakowski, R.
Stanik, Z.
Powiązania:
https://bibliotekanauki.pl/articles/245654.pdf
Data publikacji:
2016
Wydawca:
Instytut Techniczny Wojsk Lotniczych
Tematy:
rotational system
nonlinear differential system of equation
perturbation method
critical states
analytical solutions
Opis:
The paper presents a cross-sectional analysis of dynamics of rotating systems with different characteristics, starting from the search for solutions in an analytical way, and ending with the numerical attempt to verify the results. There is presented a problem of bending and torsional vibrations in rotational systems, using possibly the simplest model of the phenomenon. It is a heavy disk embedded on the deformable massless shaft. The rotor is symmetric and it is assumed that stiffness can be nonlinear. The analysis of vibrations occurring in rotors is made with the use of this model. This is followed by a preliminary discussion on the problem and the conclusions of the pilot studies. There are presented basic problems related to the phenomenon of lateral-torsional coupling in rotational systems with an emphasis on critical states. Formulation of the problem is the conclusion of preliminary part of the paper. Next, there are discussed the selected methods currently used to solve such problems, together with a discussion of their application in this case. In addition, there is discussed a problem of numerical or analytical character of obtained results and the range of using methods in modelling, designing and experimental studies. The next part of the paper focuses on the solution of the model presented in the introduction, using the following analytical or numerical methods: Krylov-Bogolubov, Adams and Runge-Kutta methods. There are presented assumptions, simplifications of the model, technical details of searching for solutions and the results together with a discussion of their correctness. The results, which were obtained from analysis, are polyharmonic. Due to this fact, the spectra of each solution were presented. These aspects are discussed in the context of the solving methods and motion analysis for rotor systems. The whole paper is summarized with a discussion of the results and their confrontation with reality.
Źródło:
Journal of KONES; 2016, 23, 4; 41-47
1231-4005
2354-0133
Pojawia się w:
Journal of KONES
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Existence of solutions of the Dirichlet problem for an infinite system of nonlinear differential-functional equations of elliptic type
Autorzy:
Zabawa, T.S.
Powiązania:
https://bibliotekanauki.pl/articles/255205.pdf
Data publikacji:
2005
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
infinite systems
elliptic differential-functional equations
monotone iterative technique
Chaplygin's method
Dirichlet problem
Opis:
The Dirichlet problem for an infinite weakly coupled system of semilinear differential-functional equations of elliptic type is considered. It is shown the existence of solutions to this problem. The result is based on Chaplygin's method of lower and uper functions.
Źródło:
Opuscula Mathematica; 2005, 25, 2; 333-343
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On nonlocal problems for fractional differential equations in Banach spaces
Autorzy:
Dong, X.
Wang, J.
Zhou, Y.
Powiązania:
https://bibliotekanauki.pl/articles/255742.pdf
Data publikacji:
2011
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
nonlocal problems
fractional differential equations
existence
generalized singular Gronwall inequality
fixed point method
Opis:
In this paper, we study the existence and uniqueness of solutions to the nonlocal problems for the fractional differential equation in Banach spaces. New sufficient conditions for the existence and uniqueness of solutions are established by means of fractional calculus and fixed point method under some suitable conditions. Two examples are given to illustrate the results.
Źródło:
Opuscula Mathematica; 2011, 31, 3; 341-357
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Identyfikacja manipulatora z napędem elektrycznym przy wykorzystaniu filtrów różniczkujących
Identification of the manipulator with electric drive using a differentiating filters
Autorzy:
Cedro, L.
Powiązania:
https://bibliotekanauki.pl/articles/251668.pdf
Data publikacji:
2015
Wydawca:
Instytut Naukowo-Wydawniczy TTS
Tematy:
manipulator
napęd elektryczny
filtr różniczkujący
metoda identyfikacji
electric drive
differential filter
identification method
Opis:
Artykuł przedstawia przykład identyfikacji parametrów manipulatora o jednym stopniu swobody. W pracy zamodelowano manipulator napędzany silnikiem prądu stałego w postaci dwóch równań różniczkowych. W identyfikacji wykorzystano opracowane filtry różniczkujące. Zastosowano metodę identyfikacji, która nie wymaga rozwiązywania układu równań różniczkowych tylko użycia zróżniczkowanych sygnałów. Zaprojektowano algorytm identyfikacji parametrów modelu wykorzystujący metodę najmniejszych kwadratów. Wymagany rząd użytych sygnałów zależy od równań różniczkowych opisujących obiekt. Model został zidentyfikowany i sprawdzony dla danych uzyskanych na stanowisku badawczym.
The paper presents an example of solving the parameter identification problem in case of robot with one degrees of freedom has been also presented. The parameter identification algorithm based on linear pa-rameterization of the manipulator model and the least square criteria is developed. The desired derivatives of measured signals are estimated by means of designed differentiation filters. The required derivative order depends on the order of differential equations describing the object. The model was identified and verified using measurement results obtained for a real system.
Źródło:
TTS Technika Transportu Szynowego; 2015, 12; 235-239, CD
1232-3829
2543-5728
Pojawia się w:
TTS Technika Transportu Szynowego
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Parameters affecting water hammer in plastic pipelines
Autorzy:
Urbanowicz, K.
Firkowski, M.
Powiązania:
https://bibliotekanauki.pl/articles/135271.pdf
Data publikacji:
2018
Wydawca:
Akademia Morska w Szczecinie. Wydawnictwo AMSz
Tematy:
water hammer
unsteady flow
viscoelastic pipes
method of characteristics
partial differential equations
creep function
Opis:
Pressure pipes made of selected plastics are widely used in current water supply systems. Unfortunately, the theoretical basis for modeling transient flows in these pipes has not been clarified yet. For simplified one-dimensional numerical modeling, a model is commonly used in which the total deformation of the pipe walls is expressed by the sum of instantaneous and retarded deformations. One of the main problems lies in the correct experimental determination of the creep function defining the properties of the polymer. The influence of other parameters on which the numerical solution of the method of characteristics is based is the subject of the research presented in this paper.
Źródło:
Zeszyty Naukowe Akademii Morskiej w Szczecinie; 2018, 54 (126); 35-43
1733-8670
2392-0378
Pojawia się w:
Zeszyty Naukowe Akademii Morskiej w Szczecinie
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Optimum design of fiber angle and hole orientation of an orthotropic plate
Autorzy:
Zhang, X.
Lu, A.
Wang, S.
Zhang, N.
Powiązania:
https://bibliotekanauki.pl/articles/280011.pdf
Data publikacji:
2018
Wydawca:
Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
Tematy:
orthotropic plate
fiber orientation angle
hole orientation angle
conformal transformation method
differential evolution algorithm
Opis:
With the goal of decreasing the stress concentration along the hole boundary in an orthotropic plate under inequi-biaxial loadings, an optimum design of the fiber angle and hole orientation is presented. The maximum absolute tangential stress along the hole boundary is taken as the objective function, and the fiber orientation angle and the hole orientation angle are considered as design variables. The conformal transformation method of a complex function and the Differential Evolution (DE) algorithm are used. Two non-circular shapes, ellipse and hexagon are taken as examples to analyze the problem. Based on the results, we can conclude that the major axis of elliptical holes should be designed in the direction of the maximum external loading for a perforated structure in an orthotropic plate. However, the principal direction that has the larger Young’s modulus should be inclined to the direction of the minimum loading, especially for a significantly orthotropic plate.
Źródło:
Journal of Theoretical and Applied Mechanics; 2018, 56, 1; 297-311
1429-2955
Pojawia się w:
Journal of Theoretical and Applied Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Existence of solution of the nonlinear Dirichlet problem for differential-functional equations of elliptic type
Autorzy:
Brzychczy, Stanisław
Powiązania:
https://bibliotekanauki.pl/articles/1311834.pdf
Data publikacji:
1993
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
nonlinear differential-functional equations of elliptic type
monotone iterative technique
Chaplygin's method
Dirichlet problem
Opis:
Consider a nonlinear differential-functional equation (1) Au + f(x,u(x),u) = 0 where $Au := ∑_{i,j=1}^m a_{ij}(x) (∂²u)/(∂x_i ∂x_j)$, $x=(x_1,...,x_m) ∈ G ⊂ ℝ^m$, G is a bounded domain with $C^{2+α}$ (0 < α < 1) boundary, the operator A is strongly uniformly elliptic in G and u is a real $L^p(G̅)$ function. For the equation (1) we consider the Dirichlet problem with the boundary condition (2) u(x) = h(x) for x∈ ∂G. We use Chaplygin's method [5] to prove that problem (1), (2) has at least one regular solution in a suitable class of functions. Using the method of upper and lower functions, coupled with the monotone iterative technique, H. Amman [3], D. H. Sattinger [13] (see also O. Diekmann and N. M. Temme [6], G. S. Ladde, V. Lakshmikantham, A. S. Vatsala [8], J. Smoller [15]) and I. P. Mysovskikh [11] obtained similar results for nonlinear differential equations of elliptic type. A special case of (1) is the integro-differential equation $Au + f(x,u(x), ∫_G u(x)dx) = 0$. Interesting results about existence and uniqueness of solutions for this equation were obtained by H. Ugowski [17].
Źródło:
Annales Polonici Mathematici; 1993, 58, 2; 139-146
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Method of lines for parabolic stochastic functional partial differential equations
Autorzy:
Ziemlańska, M.
Powiązania:
https://bibliotekanauki.pl/articles/254717.pdf
Data publikacji:
2014
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
stochastic partial differential equations
stability of method of lines
white noise
Volterra stochastic equations
Opis:
We approximate parabolic stochastic functional differential equations substituting the derivatives in the space variable by finite differences. We prove the stability of the method of lines corresponding to a parabolic SPDE driven by Brownian motion.
Źródło:
Opuscula Mathematica; 2014, 34, 2; 443-456
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Integro-differential form of the first-order dual phase lag heat transfer equation and its numerical solution using the Control Volume Method
Autorzy:
Ciesielski, M.
Mochnacki, B.
Majchrzak, E.
Powiązania:
https://bibliotekanauki.pl/articles/38606551.pdf
Data publikacji:
2020
Wydawca:
Instytut Podstawowych Problemów Techniki PAN
Tematy:
micro-scale heat transfer
dual phase lag model
integro-differential equation
Control Volume Method
Opis:
The start point of the dual phase lag equation (DPLE) formulation is the generalized Fourier law in which two positive constants (the relaxation and thermalization times) appear. This type of equation can be used (among others) to describe the heat conduction processes proceeding in micro-scale. Depending on the number of components in the development of the generalized Fourier law into a power series, one can obtain both the first-order DPLE and the second-order one. In this paper the first-order dual phase lag equation is considered. The primary objective of this research is the transformation of DPLE differential form to the integro-differential one supplemented by the appropriate boundary-initial conditions. The obtained form of the differential equation is much simpler and more convenient at the stage of numerical computations – the numerical algorithm based on the three-time-level scheme reduces to the two-time-level one. To find the numerical solution, the Control Volume Method is used (the heating of thin metal film subjected to a laser beam is considered). The choice of the numerical method was not accidental. The method has a simple physical interpretation ensuring the preservation of the local and global energy balances. To our knowledge, it has not been used so far in this type of tasks. In the final part of the paper the examples of numerical simulations are presented and the conclusions are formulated.
Źródło:
Archives of Mechanics; 2020, 72, 5; 415-444
0373-2029
Pojawia się w:
Archives of Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The homotopy analysis Rangaig transform method for nonlinear partial differential equations
Autorzy:
Ziane, Djelloul
Cherif, Mountassir Hamdi
Powiązania:
https://bibliotekanauki.pl/articles/2175522.pdf
Data publikacji:
2022
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
Rangaig transform method
homotopy analysis method
nonlinear partial differential equations
metoda transformacji Rangaiga
metoda analizy homotopii
nieliniowe równania różniczkowe cząstkowe
Opis:
The idea suggested in this article is to combine the Rangaig transform with the homotopy analysis method in order to facilitate the solution of nonlinear partial differentia equations. This method may be called the homotopy analysis Rangaig transform method (HARTM). The proposed example results showed that HARTM is an effective method for solving nonlinear partial differential equations.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2022, 21, 2; 111--122
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Analytical Solution to Linear Conformable Fractional Partial Differential Equations
Autorzy:
Dixit, Ajay
Ujlayan, Amit
Powiązania:
https://bibliotekanauki.pl/articles/1159232.pdf
Data publikacji:
2018
Wydawca:
Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
Tematy:
Conformable fractional derivative
Fractional partial differential equation
Katugampola’s derivative
Method of separation of variables
Opis:
An analytical solution is better than an approximate or series solution of a problem. Here we develop an analytical formulation to solve linear fractional order partial differential equations with given boundary conditions. We discuss the method for the simultaneous fractional derivative, in space as well as time and up to order two. Examples reflect the effectiveness and simplicity of the method. First we convert the fractional derivative into integer order derivative and then use method of separation of variables in usual sense to get the complete solution. The fractional derivative has been taken in the sense of Katugampola’s derivative.
Źródło:
World Scientific News; 2018, 113; 49-56
2392-2192
Pojawia się w:
World Scientific News
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
New iterative method of solving nonlinear equations in fluid mechanics
Autorzy:
Palivets, M.
Andreev, E.
Bakshtanin, A.
Benin, D.
Snezhko, V.
Powiązania:
https://bibliotekanauki.pl/articles/2106452.pdf
Data publikacji:
2021
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
trzęsienie ziemi
mechanika płynów
porowatość
Adomian Decomposition Method ADM
earthquake
filtration
fluid mechanics
iterative method
nonlinear fractional partial differential equations
porous medium
Opis:
This paper presents the results of applying a new iterative method to linear and nonlinear fractional partial differential equations in fluid mechanics. A numerical analysis was performed to find an exact solution of the fractional wave equation and fractional Burgers’ equation, as well as an approximate solution of fractional KdV equation and fractional Boussinesq equation. Fractional derivatives of the order are described using Caputo's definition with 01<α≤ or 12<α≤. A comparative analysis of the results obtained using a new iterative method with those obtained by the Adomian decomposition method showed the first method to be more efficient and simple, providing accurate results in fewer computational operations. Given its flexibility and ability to solve nonlinear equations, the iterative method can be used to solve more complex linear and nonlinear fractional partial differential equations.
Źródło:
International Journal of Applied Mechanics and Engineering; 2021, 26, 3; 163--176
1734-4492
2353-9003
Pojawia się w:
International Journal of Applied Mechanics and Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Solution approaches to differential equations of mechanical system dynamics: a case study of car suspension system
Autorzy:
Terefe, Tesfaye O.
Lemu, Hirpa G
Powiązania:
https://bibliotekanauki.pl/articles/102050.pdf
Data publikacji:
2018
Wydawca:
Stowarzyszenie Inżynierów i Techników Mechaników Polskich
Tematy:
numerical method
Euler method
differential equation
suspension system
MATLAB
mechanical system modeling
metoda numeryczna
Metoda Eulera
równanie różniczkowe
zawieszenie
modelowanie układów mechanicznych
Opis:
Solution of a dynamic system is commonly demanding when analytical approaches are used. In order to solve numerically, describing the motion dynamics using differential equations is becoming indispensable. In this article, Newton’s second law of motion is used to derive the equation of motion the governing equation of the dynamic system. A quarter model of the suspension system of a car is used as a case and sinusoidal road profile input was considered for modeling. The state space representation was used to reduce the second order differential equation of the dynamic system of suspension model to the first order differential equation. Among the available numerical methods to solve differential equations, Euler method has been employed and the differential equation is coded MATLAB. The numerical result of the second degree of freedom, quarter suspension system demonstrated that the approach of using numerical solution to a differential equation of dynamic system is suitable to easily simulate and visualize the system performance.
Źródło:
Advances in Science and Technology. Research Journal; 2018, 12, 2; 266-273
2299-8624
Pojawia się w:
Advances in Science and Technology. Research Journal
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Stability of solutions of infinite systems of nonlinear differential-functional equations of parabolic type
Autorzy:
Zabawa, T.S.
Powiązania:
https://bibliotekanauki.pl/articles/254967.pdf
Data publikacji:
2006
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
stability of solutions
infinite systems
parabolic equations
elliptic equations
semilinear differential-functional equations
monotone iteration method
Opis:
A parabolic initial boundary value problem and an associated elliptic Dirichlet problem for an infinite weakly coupled system of semilinear differential-functional equations are considered. It is shown that the solutions of the parabolic problem is asymptotically stable and the limit of the solution of the parabolic problem as t → ∞ is the solution of the associated elliptic problem. The result is based on the monotone methods.
Źródło:
Opuscula Mathematica; 2006, 26, 1; 173-183
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Bounded, asymptotically stable, and L1 solutions of caputo fractional differential equations
Autorzy:
Islam, M.N.
Powiązania:
https://bibliotekanauki.pl/articles/255179.pdf
Data publikacji:
2015
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
Caputo fractional differential equations
Volterra integral equations
weakly singular kernel
Schauder fixed point theorem
Liapunov's method
Opis:
The existence of bounded solutions, asymptotically stable solutions, and L1 solutions of a Caputo fractional differential equation has been studied in this paper. The results are obtained from an equivalent Volterra integral equation which is derived by inverting the fractional differential equation. The kernel function of this integral equation is weakly singular and hence the standard techniques that are normally applied on Volterra integral equations do not apply here. This hurdle is overcomed using a resolvent equation and then applying some known properties of the resolvent. In the analysis Schauder's fixed point theorem and Liapunov's method have been employed. The existence of bounded solutions are obtained employing Schauder's theorem, and then it is shown that these solutions are asymptotically stable by a definition found in [C. Avramescu, C. Vladimirescu, On the existence of asymptotically stable solution of certain integral equations, Nonlinear Anal. 66 (2007), 472-483]. Finally, the L1 properties of solutions are obtained using Liapunov's method
Źródło:
Opuscula Mathematica; 2015, 35, 2; 181-190
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Stabilized model reduction for nonlinear dynamical systems through a contractivity-preserving framework
Autorzy:
Chaturantabut, Saifon
Powiązania:
https://bibliotekanauki.pl/articles/1838159.pdf
Data publikacji:
2020
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
model order reduction
ordinary differential equation
partial differential equation
proper orthogonal decomposition
discrete empirical interpolation method
redukcja rzędu modelu
równanie różniczkowe zwyczajne
równanie różniczkowe cząstkowe
rozkład ortogonalny
Opis:
This work develops a technique for constructing a reduced-order system that not only has low computational complexity, but also maintains the stability of the original nonlinear dynamical system. The proposed framework is designed to preserve the contractivity of the vector field in the original system, which can further guarantee stability preservation, as well as provide an error bound for the approximated equilibrium solution of the resulting reduced system. This technique employs a low-dimensional basis from proper orthogonal decomposition to optimally capture the dominant dynamics of the original system, and modifies the discrete empirical interpolation method by enforcing certain structure for the nonlinear approximation. The efficiency and accuracy of the proposed method are illustrated through numerical tests on a nonlinear reaction diffusion problem.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2020, 30, 4; 615-628
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A Nash equilibrium approach for multiobjective optimal control problems with elliptic partial differential equations
Autorzy:
Dreves, A.
Powiązania:
https://bibliotekanauki.pl/articles/206122.pdf
Data publikacji:
2016
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
multiobjective optimization
generalized Nash equilibrium
optimal control problem
elliptic partial differential equation
finite elements
interior point method
Opis:
We consider the generalized Nash equilibrium as a solution concept for multiobjective optimal control problems governed by elliptic partial differential equations with constraints not only for the control but also for the state variables. In the first part, we present a constructive proof of the existence of a generalized Nash equilibrium via an approximating sequence of suitable finite dimensional discretizations. In the second part, we propose a variant of a potential reduction algorithm for the numerical solution of these discretized problems. In contrast to the existing numerical approaches ours does not require the computation of the control–to–state mapping. Instead we introduce different state variables and guarantee that they become equal at a solution. We prove sufficient conditions for the convergence of our algorithm to a solution. Furthermore, some numerical results showing the applicability are provided.
Źródło:
Control and Cybernetics; 2016, 45, 4; 457-482
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The implicit numerical method for the one-dimensional anomalous subdiffusion equation with a nonlinear source term
Autorzy:
Błasik, Marek
Powiązania:
https://bibliotekanauki.pl/articles/2086846.pdf
Data publikacji:
2021
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
fractional derivative
fractional integral
integro-differential equations
numerical method
finite difference method
pochodna ułamkowa
całkowanie ułamkowe
równanie całkowo-różniczkowe
metoda numeryczna
metoda elementów skończonych
Opis:
In the paper, the numerical method of solving the one-dimensional subdiffusion equation with the source term is presented. In the approach used, the key role is played by transforming of the partial differential equation into an equivalent integro-differential equation. As a result of the discretization of the integro-differential equation obtained an implicit numerical scheme which is the generalized Crank-Nicolson method. The implicit numerical schemes based on the finite difference method, such as the Carnk-Nicolson method or the Laasonen method, as a rule are unconditionally stable, which is their undoubted advantage. The discretization of the integro-differential equation is performed in two stages. First, the left-sided Riemann-Liouville integrals are approximated in such a way that the integrands are linear functions between successive grid nodes with respect to the time variable. This allows us to find the discrete values of the integral kernel of the left-sided Riemann-Liouville integral and assign them to the appropriate nodes. In the second step, second order derivative with respect to the spatial variable is approximated by the difference quotient. The obtained numerical scheme is verified on three examples for which closed analytical solutions are known.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2021, 69, 6; e138240, 1--9
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A finite difference method for nonlinear parabolic-elliptic systems of second-order partial differential equations
Autorzy:
Malec, M.
Sapa, L.
Powiązania:
https://bibliotekanauki.pl/articles/255499.pdf
Data publikacji:
2007
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
partial differential equation
parabolic-elliptic system
finite difference method
finite difference scheme
consistence
convergence
stability
error estimate
uniqueness
Opis:
This paper deals with a finite difference method for a wide class of weakly coupled nonlinear second-order partial differential systems with initial condition and weakly coupled nonlinear implicit boundary conditions. One part of each system is of the parabolic type (degenerated parabolic equations) and the other of the elliptic type (equations with a parameter) in a cube in R1+n. A suitable finite difference scheme is constructed. It is proved that the scheme has a unique solution, and the numerical method is consistent, convergent and stable. The error estimate is given. Moreover, by the method, the differential problem has at most one classical solution. The proof is based on the Banach fixed-point theorem, the maximum principle for difference functional systems of the parabolic type and some new difference inequalities. It is a new technique of studying the mixed-type systems. Examples of physical applications and numerical experiments are presented.
Źródło:
Opuscula Mathematica; 2007, 27, 2; 259-289
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Analytical solution of the time fractional Fokker-Planck equation
Autorzy:
Sutradhar, T.
Datta, B. K.
Bera, R. K.
Powiązania:
https://bibliotekanauki.pl/articles/955129.pdf
Data publikacji:
2014
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
równanie Fokkera-Plancka
równania różniczkowe
mechanika stosowana
Fokker-Planck equation
Adomian decomposition method
fractional calculus
fractional differential equation
Opis:
A nonperturbative approximate analytic solution is derived for the time fractional Fokker-Planck (F-P) equation by using Adomian’s Decomposition Method (ADM). The solution is expressed in terms of Mittag-Leffler function. The present method performs extremely well in terms of accuracy, efficiency and simplicity.
Źródło:
International Journal of Applied Mechanics and Engineering; 2014, 19, 2; 435-440
1734-4492
2353-9003
Pojawia się w:
International Journal of Applied Mechanics and Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Successive iterative method for higher-order fractional differential equations involving Stieltjes integral boundary conditions
Autorzy:
Jankowski, T.
Powiązania:
https://bibliotekanauki.pl/articles/1938598.pdf
Data publikacji:
2016
Wydawca:
Politechnika Gdańska
Tematy:
fractional differential equations with delayed arguments
Stieltjes integral boundary conditions
successive iterative method
convergence
existence of positive solutions
Opis:
In this paper, the existence of positive solutions to fractional differential equations with delayed arguments and Stieltjes integral boundary conditions is discussed. The convergence of successive iterative method of solving such problems is investigated. This allows us to improve some recent works. Some numerical examples illustrate the results.
Źródło:
TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk; 2016, 20, 1; 99-108
1428-6394
Pojawia się w:
TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The mathematical characteristic of the Laplace contour filters used in digital image processing. The third order filters
Autorzy:
Winnicki, Ireneusz
Jasinski, Janusz
Pietrek, Sławomir
Kroszczynski, Krzysztof
Powiązania:
https://bibliotekanauki.pl/articles/43852806.pdf
Data publikacji:
2022
Wydawca:
Polska Akademia Nauk. Czasopisma i Monografie PAN
Tematy:
metoda elementów skończonych
filtr Laplace'a
równanie różniczkowe
transfer function
finite element method
finite difference method
matrices of the third-order Laplace filters
modified differential equations
Opis:
The Laplace operator is a differential operator which is used to detect edges of objects in digital images. This paper presents the properties of the most commonly used third-order 3x3 pixels Laplace contour filters including the difference schemes used to derive them. The authors focused on the mathematical properties of the Laplace filters. The basic reasons of the differences of the properties were studied and indicated using their transfer functions and modified differential equations. The relations between the transfer function for the differential Laplace operator and its difference operators were described and presented graphically. The impact of the corner elements of the masks on the results was discussed. This is a theoretical work. The basic research conducted here refers to a few practical examples which are illustrations of the derived conclusions.We are aware that unambiguous and even categorical final statements as well as indication of areas of the results application always require numerous experiments and frequent dissemination of the results. Therefore, we present only a concise procedure of determination of the mathematical properties of the Laplace contour filters matrices. In the next paper we shall present the spectral characteristic of the fifth order filters of the Laplace type.
Źródło:
Advances in Geodesy and Geoinformation; 2022, 71, 2; art. no. e23, 2022
2720-7242
Pojawia się w:
Advances in Geodesy and Geoinformation
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Discrete relaxed method for semilinear parabolic optimal control problem
Autorzy:
Chryssoverghi, I.
Coletsos, J.
Kokkinis, B.
Powiązania:
https://bibliotekanauki.pl/articles/205973.pdf
Data publikacji:
1999
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
sterowanie optymalne
accumulation points
discrete optimisation method
discretization
distributed control
minimum principle
optimal control
parabolic equations
partial differential equations
penalty method
relaxed control
semilinear parabolic system
Opis:
We consider an optimal control problem for systems governed by semilinear parabolic partial differential equations with control and state constraints, without any convexity assumptions. A discrete optimization method is proposed to solve this problem in its relaxed form which combines a penalized Armijo type method with a finite element discretization and constructs sequences of discrete Gamkrelidze relaxed controls. Under appropriate assumptions, we prove that accumulation points of these sequences satisfy the relaxed Pontryagin necessary conditions for optimality. Moreover, we show that the Gamkrelidze controls thus generated can be replaced by simulating piecewise constant classical controls.
Źródło:
Control and Cybernetics; 1999, 28, 2; 157-176
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A differential evolution approach to dimensionality reduction for classification needs
Autorzy:
Martinović, G.
Bajer, D.
Zorić, B.
Powiązania:
https://bibliotekanauki.pl/articles/331498.pdf
Data publikacji:
2014
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
classification
differential evolution
feature subset selection
k-nearest neighbour algorithm
wrapper method
ewolucja różnicowa
selekcja cech
algorytm najbliższego sąsiada
Opis:
The feature selection problem often occurs in pattern recognition and, more specifically, classification. Although these patterns could contain a large number of features, some of them could prove to be irrelevant, redundant or even detrimental to classification accuracy. Thus, it is important to remove these kinds of features, which in turn leads to problem dimensionality reduction and could eventually improve the classification accuracy. In this paper an approach to dimensionality reduction based on differential evolution which represents a wrapper and explores the solution space is presented. The solutions, subsets of the whole feature set, are evaluated using the k-nearest neighbour algorithm. High quality solutions found during execution of the differential evolution fill the archive. A final solution is obtained by conducting k-fold cross-validation on the archive solutions and selecting the best one. Experimental analysis is conducted on several standard test sets. The classification accuracy of the k-nearest neighbour algorithm using the full feature set and the accuracy of the same algorithm using only the subset provided by the proposed approach and some other optimization algorithms which were used as wrappers are compared. The analysis shows that the proposed approach successfully determines good feature subsets which may increase the classification accuracy.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2014, 24, 1; 111-122
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Impact of Energy Slope Averaging Methods on Numerical Solution of 1D Steady Gradually Varied Flow
Autorzy:
Artichowicz, W.
Prybytak, D.
Powiązania:
https://bibliotekanauki.pl/articles/240952.pdf
Data publikacji:
2015
Wydawca:
Polska Akademia Nauk. Instytut Budownictwa Wodnego PAN
Tematy:
standard step method
numerical integration
initial-value problem
ordinary differential equation
open channel
steady gradually varied flow
energy slope
Opis:
In this paper, energy slope averaging in the one-dimensional steady gradually varied flow model is considered. For this purpose, different methods of averaging the energy slope between cross-sections are used. The most popular are arithmetic, geometric, harmonic and hydraulic means. However, from the formal viewpoint, the application of different averaging formulas results in different numerical integration formulas. This study examines the basic properties of numerical methods resulting from different types of averaging.
Źródło:
Archives of Hydro-Engineering and Environmental Mechanics; 2015, 62, 3-4; 101-119
1231-3726
Pojawia się w:
Archives of Hydro-Engineering and Environmental Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Numerical scheme methods for solving nonlinear pseudo-hyperbolic partial differential equations
Autorzy:
Abdulazeez, Sadeq Taha
Modanli, Mahmut
Husien, Ahmad Muhamad
Powiązania:
https://bibliotekanauki.pl/articles/2202054.pdf
Data publikacji:
2022
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
nonlinear pseudo-hyperbolic partial differential equation
homotopy analysis method
variational iteration method
approximate solution
nieliniowe pseudohiperboliczne równanie różniczkowe cząstkowe
homotopijna metoda analizy
metoda iteracji wariacyjnych
rozwiązanie przybliżone
Opis:
The numerical solutions to the nonlinear pseudo-hyperbolic partial differentia equation with nonlocal conditions are presented in this study. This equation is solved using the homotopy analysis technique (HAM) and the variational iteration method (VIM). Both strategies are compared and contrasted in terms of approximate and accurate solutions. The results show that the HAM technique is more appropriate, effective, and close to the exact solution than the VIM method. Finally, the graphical representations of the obtained results are given.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2022, 21, 4; 5--15
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Application of LDG scheme to solve semi-differential equations
Autorzy:
Izadi, Mohammad
Powiązania:
https://bibliotekanauki.pl/articles/122346.pdf
Data publikacji:
2019
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
Caputo fractional derivative
local discontinuous Galerkin method
semi-differential equations
pochodna ułamkowa Caputo
nieciągła metoda Galerkina
schemat LDG
równania różnicowe
Opis:
In the current work, we investigate a technique based on discontinuous Galerkin method for the numerical approximation of semi-differential equations with Caputo’s fractional derivative. In this approach, using the natural upwind fluxes enables us to solve the model problem element by element locally in each subintervals and there is no need to solve a full global matrix. Numerical experiments are given to verify the efficiency and accuracy of the proposed method. Numerical solutions are compared with the exact solutions as well as the numerical solutions obtained by other available well-established computational procedures. The results show that the LDG method is more accurate for solving this class of differential equation with relatively low degrees of polynomials and number of elements.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2019, 18, 4; 27-39
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Numerical study for a second order Fredholm integro-differential equation by applying Galerkin-Chebyshev-wavelets method
Autorzy:
Henka, Youcef
Lemita, Samir
Aissaoui, Mohamed-Zine
Powiązania:
https://bibliotekanauki.pl/articles/2202040.pdf
Data publikacji:
2022
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
Fredholm integro-differential equations
nonlinear equation
Galerkin method
Chebyshev wavelets
równanie całkowo-różniczkowe Fredholma
równanie nieliniowe
metoda Galerkina
falki Czebyszewa
Opis:
In the present paper, we apply the Galerkin method using Chebyshev wavelets to approximate the exact solution for a second order Fredholm integro-differential equation with initial conditions. This numerical method gives us a nonlinear algebraic system that would be solved using the Picard successive approximations technique. Furthermore, we show the validity and the ability of the proposed method through some illustrative examples.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2022, 21, 4; 28--39
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
JMATRIX - package for relativistic J-MATRIX calculations in elastic scattering of electrons from model potentials
Autorzy:
Syty, P.
Sienkiewicz, J. E.
Powiązania:
https://bibliotekanauki.pl/articles/1940696.pdf
Data publikacji:
2017
Wydawca:
Politechnika Gdańska
Tematy:
J-matrix method
relativistic
electron elastic scattering
phase shifts
Dirac partial-waves analysis
differential
total
momentum transfer
spin polarization cross sections
Opis:
We present a software package JMATRIX, consisting of two computer codes written in FORTRAN 95 and parallelized with OpenMP, implementing the so-called J-matrix method, applied to elastic scattering of electrons on the radial potential, vanishing faster than the Coulomb potential. In the J-matrix method, the physical scattering problem is replaced by using a well-defined model which is solved analytically. The presented software implements both non-relativistic and relativistic versions of the method, and allows calculations of scattering phase shifts as well as cross sections, in cases when the scattering potential is given through an analytical formula. We performed test calculations for the scattering potential modeled as a truncated Coulomb potential. We show that the numerical phase shifts to converge as we increase the size of the basis used to truncate the scattering potential, and that the method is suitable for calculating the total differential momentum transfer and spin polarization cross sections, using the partial-wave analysis.
Źródło:
TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk; 2017, 21, 1; 17-42
1428-6394
Pojawia się w:
TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Investigation on numerical solution for a robot arm problem
Autorzy:
Ponalagusamy, R.
Senthilkumar, S.
Powiązania:
https://bibliotekanauki.pl/articles/384690.pdf
Data publikacji:
2009
Wydawca:
Sieć Badawcza Łukasiewicz - Przemysłowy Instytut Automatyki i Pomiarów
Tematy:
Runge-Kutta (RK) method
RK-Arithmetic mean
RK- Fifth order algorithm
RK-Sixth order algorithm
Differential Equations (ODE)
robot arm problem
Opis:
The aim of this article is focused on providing numerical solutions for a Robot arm problem using the Runge-Kutta sixth-order algorithm. The parameters involved in problem of a Robot control have also been discussed through RKsixth-order algorithm. The précised solution of the system of equations representing the arm model of a robot has been compared with the corresponding approximate solutions at different time intervals. Experimental results and comparison show the efficiency of the numerical integration algorithm based on the absolute error between the exact and approximate solutions. The stability polynomial for the test equation ( is a complex Number) using RK-Butcher algorithm obtained by Murugesan et. al. [Murugesan K., Sekar S., Murugesh V., Park J.Y., "Numerical solution of an Industrial Robot arm Control Problem using the RK-Butcher Algorithm", International Journal of Computer Applications in Technology, vol.19, no. 2, 2004, pp. 132-138] is not correct and the stability regions for RK-fourth order (RKAM) and RK-Butcher methods have been presented incorrectly. They have made a mistake in determining the range for real parts of (h is a step size) involved in the test equation for RKAM and RK-Butcher algorithms. In the present paper, a corrective measure has been taken to obtain the stability polynomial for the case of RK-Butcher algorithm, the ranges for the real part of and to present graphically the stability regions of the RKAM and the RK-Butcher methods. The stability polynomial and stability region of RK-Sixth order are also reported. Based on the numerical results it is observed that the error involved in the numerical solution obtained by RK-Sixth order is less in comparison with that obtained by the RK-Fifth order and RK-Fourth order respectively.
Źródło:
Journal of Automation Mobile Robotics and Intelligent Systems; 2009, 3, 3; 34-40
1897-8649
2080-2145
Pojawia się w:
Journal of Automation Mobile Robotics and Intelligent Systems
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On some topological methods in theory of neutral type operator differential inclusions with applications to control systems
Autorzy:
Kamenskii, Mikhail
Obukhovskii, Valeri
Yao, Jen-Chih
Powiązania:
https://bibliotekanauki.pl/articles/729536.pdf
Data publikacji:
2013
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
operator differential inclusion
neutral type
periodic solution
fixed point
multivalued map
condensing map
topological degree
averaging method
control system
distributed control
Opis:
We consider a neutral type operator differential inclusion and apply the topological degree theory for condensing multivalued maps to justify the question of existence of its periodic solution. By using the averaging method, we apply the abstract result to an inclusion with a small parameter. As example, we consider a delay control system with the distributed control.
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2013, 33, 2; 193-204
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Variation of parameters method for a three-dimensional problem of condensation film on an inclined rotating disk
Autorzy:
Güngör, Osman
Arslantürk, Cihat
Powiązania:
https://bibliotekanauki.pl/articles/122445.pdf
Data publikacji:
2019
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
condensation
rotating inclined disk
nonlinear ordinary differential equations
variation of parameters method
VPM
kondensacja
nieliniowe równania różniczkowe zwyczajne
metoda zmiany parametrów
Opis:
In this paper, the steady three-dimensional problem of condensation film on an inclined rotating disk is considered. The governing nonlinear partial differential equations are reduced to the nonlinear ordinary differential equations system by a similarity transform. The equation system is solved by the variation of parameters method (VPM) which is rather used to solve nonhomogeneous linear differential equations but can also be used to solve nonlinear differential equations. This method has not previously been used to solve a nonlinear condensation problem. The dimensionless velocity and temperature profiles are shown, and the influence of Prandtl number and rotation ratio on the flow field and the Nusselt number are discussed in detail. In order to assess the accuracy of the solutions obtained by this method, the problem is also solved numerically using the Matlab bvp4c solver. The validity of our solutions is verified by the numerical results.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2019, 18, 1; 15-28
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Mathematical modeling of the process of drawing an optical fiber using the Langevin equation
Modelowanie matematyczne procesu wyciągania światłowodu wykorzystujące równanie Langevina
Autorzy:
Tergeussizova, Aliya
Powiązania:
https://bibliotekanauki.pl/articles/407870.pdf
Data publikacji:
2019
Wydawca:
Politechnika Lubelska. Wydawnictwo Politechniki Lubelskiej
Tematy:
transport delay
object with delay
dynamic compensation method
Langevin differential equation
opóźnienie transportu
opóźnienie obiektu
metoda kompensacji dynamicznej
równanie różniczkowe Langevina
Opis:
In order to design stochastic pulse frequency systems for automatic control of objects with delay, this article shows how we obtained their models in the form of stochastic differential equations. The method of dynamic compensation of objects with delay is considered. A stochastic differential system in the Langevin form is obtained.
W celu zaprojektowania stochastycznych systemów impulsowych przeznaczonych do automatycznego sterowania obiektami z opóźnieniem pokazano, jak uzyskano te modele w postaci stochastycznych równań różniczkowych. Rozważano metodę dynamicznej kompensacji obiektów z opóźnieniem. Uzyskano stochastyczny układ różnicowy w postaci Langevina.
Źródło:
Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska; 2019, 9, 2; 64-67
2083-0157
2391-6761
Pojawia się w:
Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The mathematical characteristic of the fifth order Laplace contour filters used in digital image processing
Autorzy:
Winnicki, Ireneusz
Pietrek, Sławomir
Jasinski, Janusz
Kroszczynski, Krzysztof
Powiązania:
https://bibliotekanauki.pl/articles/43852793.pdf
Data publikacji:
2022
Wydawca:
Polska Akademia Nauk. Czasopisma i Monografie PAN
Tematy:
metoda elementów skończonych
równanie różniczkowe
filtr Laplace'a
finite element method
finite difference method
modified differential equations
matrices of the fifth-order Laplace filter
Taylor expansion of the transfer function
Opis:
The Laplace operator is a differential operator which is used to detect edges of objects in digital images. This paper presents the properties of the most commonly used fifth-order pixels Laplace filters including the difference schemes used to derive them (finite difference method – FDM and finite element method – FEM). The results of the research concerning third-order pixels matrices of the convolution Laplace filters used for digital processing of images were presented in our previous paper: The mathematical characteristic of the Laplace contour filters used in digital image processing. The third order filters is presented byWinnicki et al. (2022). As previously, the authors focused on the mathematical properties of the Laplace filters: their transfer functions and modified differential equations (MDE). The relations between the transfer function for the differential Laplace operator and its difference operators are described and presented here in graphical form. The impact of the corner elements of the masks on the results is also discussed. A transfer function, is a function characterizing properties of the difference schemes applied to approximate differential operators. Since they are relations derived in both types of spaces (continuous and discrete), comparing them facilitates the assessment of the applied approximation method.
Źródło:
Advances in Geodesy and Geoinformation; 2022, 71, 2; art. no. e26, 2022
2720-7242
Pojawia się w:
Advances in Geodesy and Geoinformation
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Eigenvalue-eigenfunction problem for Steklovs smoothing operator and differential-difference equations of mixed type
Autorzy:
Iakovlev, S. I.
Iakovleva, V.
Powiązania:
https://bibliotekanauki.pl/articles/254795.pdf
Data publikacji:
2013
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
Steklov's smoothing operator
spectrum
eigenvalues
eigenfunctions
mixed-type differential-difference equations
initial function
method of steps
countably normed space
transformation group
generator
Opis:
It is shown that any μ ∈ C is an infinite multiplicity eigenvalue of the Steklov smoothing operator Sh acting on the space [formula]. For μ ≠ 0 the eigenvalue-eigenfunction problem leads to studying a differential-difference equation of mixed type. An existence and uniqueness theorem is proved for this equation. Further a transformation group is defined on a countably normed space of initial functions and the spectrum of the generator of this group is studied. Some possible generalizations are pointed out.
Źródło:
Opuscula Mathematica; 2013, 33, 1; 81-98
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Monotone iterative methods for infinite systems of reaction-diffusion-convection equations with functional dependence
Autorzy:
Brzychczy, S.
Powiązania:
https://bibliotekanauki.pl/articles/255097.pdf
Data publikacji:
2005
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
infinite systems
reaction-diffusion-convection equations
semilinear parabolic differential-functional equations
Volterra functionals
monotone iterative methods
method of upper and lower solutions
Opis:
We consider the Fourier first initial-boundary value problem for an infinite system of semilinear parabolic differential-functional equations of reaction-diffusion-convection type of the form [formula] where [formula] in a bounded cylindrical domain (0, T] x G := D rcup Rm+1. The right-hand sides of the system are Volterra type functionals of the unknown function z. In the paper, we give methods of the construction of the monotone iterative sequences converging to the unique classical solution of the problem considered in partially ordered Banach spaces with various convergence rates of iterations. We also give remarks on monotone iterative methods in connection with numerical methods, remarks on methods for the construction of lower and upper solutions and remarks concerning the possibility of extending these methods to more general parabolic equations. All monotone iterative methods are based on differential inequalities and, in this paper, we use the theorem on weak partial differential-functional inequalities for infinite systems of parabolic equations, the comparison theorem and the maximum principle. A part of the paper is based on the results of our previous papers. These results generalize the results obtained by several authors in numerous papers for finite systems of semilinear parabolic differential equations to encompass the case of infinite systems of semilinear parabolic differential-functional equations. The monotone iterative schemes can be used for the computation of numerical solutions.
Źródło:
Opuscula Mathematica; 2005, 25, 1; 29-99
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Dropping liquid time-dependent flow in a pipe of lengthwise linearly varying diameter
Przepływ spadającej cieczy zależny od czasu w rurze o podłużnie liniowo zmiennej średnicy
Autorzy:
Sarukhanyan, T. A.
Powiązania:
https://bibliotekanauki.pl/articles/2068338.pdf
Data publikacji:
2013
Wydawca:
Politechnika Częstochowska
Tematy:
przepływ cieczy
rura sztywna
rura stożkowa
metoda zmiennych rozłącznych
równanie różniczkowe
liquid flow
rigid pipe
conical pipe
separable variables method
differential equation
Opis:
The objective of this paper is to discuss briefly unsteady flow of incompressible liquid in a rigid pipe the diameter of which is changed lengthwise by linear law. Within these conditions a differential equation was set up. To integrate the former boundary conditions were defined for speedup period of liquid flow. Instantaneous averaged velocity values for a number of cross-sections have been plotted, stabilization rate and period have been determined. The problem is particularly difficult when the flow is slow and walls of the pipe and the liquid are deformable. A set of equations characterizing interaction of pressure and rate change have been established for these conditions. A slowing non-steady flow in a narrowing conical pipe was studied. Fluid medium and walls of the pipe are considered as elastic materials. The hydraulic shock phenomena in case of instantaneous closure of a valve mounted at the end of the conical pipe connected to the reservoir has been examined. Initial and boundary conditions for the problem solution have been set up. In accordance with these conditions obtained differential equations have been integrated using the method of separable variables. Solutions of equations were sought for in the form of infinite series wherein values of participating factors have been obtained from respective boundary conditions. This solution enables to obtain the measure of pressure rise at the end of a conical pipe in case the valve is suddenly closed. The suggested technique enables to solve similar in nature problems in case of different boundary conditions.
Celem niniejszego artykułu jest zwięzłe omówienie nierównomiernego przepływu nieściśliwej cieczy w sztywnej rurze, której średnica jest podłużnie, liniowo zmienna. Przy tak określonych warunkach zostało wyprowadzone równanie różniczkowe. W celu zintegrowania dotychczasowych warunków brzegowych zostało określone przyspieszenie okresu przepływu cieczy. Uśrednione wartości prędkości chwilowych dla wielu przekrojów zostały przedstawione na wykresach. Ponadto określono współczynnik i okres stabilizacji. Problem ten jest szczególnie trudny, gdy przepływ jest powolny i ścianki rury są odkształcalne. Został określony układ równań charakteryzujących oddziaływanie ciśnienia i zmiany współczynników dla przyjętych warunków. Zbadano spowolnienie nierównomiernego przepływu w rurze zwężonej stożkowo. Nośnik płynu i ściany rury rozpatrywano jako materiały sprężyste. Przeanalizowano zjawisko uderzenia hydraulicznego w przypadku chwilowego zamknięcia zaworu, zamontowanego na końcu rury stożkowej, połączonej ze zbiornikiem. Zostały ustalone początkowe i brzegowe warunki rozwiązania problemu. Zgodnie z tymi warunkami otrzymane równania różniczkowe połączono z wykorzystaniem metody zmiennych rozłącznych. Rozwiązania równań były poszukiwane w postaci nieskończonej serii, w której wartości czynników uczestniczących zostały uzyskane z odpowiednich warunków brzegowych. To rozwiązanie pozwala na uzyskanie wartości wzrostu ciśnienia na końcu rury stożkowej w przypadku nagłego zamknięcia zaworu. Sugerowana technika pozwala rozwiązać podobne problemy w przypadku różnych warunków brzegowych.
Źródło:
Zeszyty Naukowe Politechniki Częstochowskiej. Budownictwo; 2013, 19 (169); 163--170
0860-7214
Pojawia się w:
Zeszyty Naukowe Politechniki Częstochowskiej. Budownictwo
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Existence and convergence results for Caputo fractional Volterra integro-differential equations
Autorzy:
Hamoud, A. A.
Bani Issa, M. Sh.
Ghadle, K. P.
Abdulghani, M.
Powiązania:
https://bibliotekanauki.pl/articles/2052432.pdf
Data publikacji:
2018
Wydawca:
Politechnika Rzeszowska im. Ignacego Łukasiewicza. Oficyna Wydawnicza
Tematy:
homotopy analysis method
Caputo fractional derivative
Volterra integro-differential equation
approximate solution
homotopijna metoda analizy
pochodna ułamkowa Caputo
równanie różniczkowe Volterry
rozwiązanie przybliżone
Opis:
In this article, homotopy analysis method is successfully applied to find the approximate solution of Caputo fractional Volterra integro-differential equation. The reliability of the method and reduction in the size of the computational work give this method a wider applicability. Also, the behavior of the solution can be formally determined by analytical approximate. Moreover, we proved the existence and convergence of the solution. Finally, an example is included to demonstrate the validity and applicability of the proposed technique.
Źródło:
Journal of Mathematics and Applications; 2018, 41; 109-121
1733-6775
2300-9926
Pojawia się w:
Journal of Mathematics and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Analysis of disturbance torque influence on critical state in rotational systems
Analiza wpływu zaburzenia momentu skręcającego na stany krytyczne układów wirujących
Autorzy:
Chiliński, B.
Powiązania:
https://bibliotekanauki.pl/articles/375562.pdf
Data publikacji:
2013
Wydawca:
Politechnika Śląska. Wydawnictwo Politechniki Śląskiej
Tematy:
rotational system
nonlinear differential system of equation
analytical solutions
Galerkin method
system rotacyjny
nieliniowe równania układu różnicowego
metoda Galerkina
stany krytyczne
rozwiązania analityczne
Opis:
Currently most of existing means of transport contains different types of rotational systems. In many cases the dynamics of such rotors substantially can influence exploitation of the whole vehicle. Moreover, in order to minimize mass of the whole object modern construction materials are applied. This causes that the dynamic phenomena may be fundamental of exploitation. The paper presents preliminary analysis of disturbance torque influence on critical state in rotational system. The consideration assumed simple physical object in the form of heavy disk embedded on weightless, elastic shaft. The shaft was supported on two bearings. In particular chapters of paper, path leading from proposition of physical model, by solution of it, to qualitative conclusions about considered object and torque disturbances influence of motion of this system, was presented. In introduction, outline of considered problem and potential opportunities of it, were demonstrated. In the next chapter, physical and mathematical model of the analysed object, was described. Next and also the last but one chapter gives a detailed discussion of mathematical model in the form of nonlinear ordinary differential equations proposed earlier. The first part of the chapter presents the possibility to solve such a problem, then it shows the simplifications which are used. Furthermore, the influence of used simplifications on the shape of analysed problem was demonstrated. Additionally, the possibility of equations solution presented in the paper was discussed. Moreover, the series of interesting properties of analysed system of equations has been shown based on founded approximate solutions. The whole paper was summarized with plans for future work and synthetic conclusions concerning the innovative control method of critical states.
Aktualnie większość istniejących środków transportu zawiera różnego typu układy wirujące. W wielu przypadkach dynamika takich wirników w istotny sposób wpływa na eksploatacje całego pojazdu. Ponadto w celu zminimalizowania masy całego obiektu stosuje się nowoczesne materiały konstrukcyjne. To powoduje, że zjawiska dynamiczne, mogą mieć podstawowe znaczenie eksploatacyjne. Artykuł przedstawia wstępną analizę wpływu zaburzenia momentu skręcającego na stany krytyczne układu wirującego. Do rozważań przyjęto prosty obiekt fizyczny w postaci ciężkiego krążka osadzonego na nieważkim podatnym wale podpartym w dwóch łożyskach. W poszczególnych rozdziałach artykułu przedstawiono drogę prowadzącą od zaproponowania modelu fizycznego, przez jego rozwiązanie do jakościowych wniosków o rozpatrywanym obiekcie i wpływie zaburzenia momentu skręcającego na jego ruch. We wstępie przedstawiono zarys rozpatrywanego problemu oraz potencjalne możliwości wykorzystania opracowanego zagadnienia. W kolejnym rozdziale zaprezentowano model fizyczny oraz matematyczny dla obiektu będącego podstawą niniejszego artykułu. Następny i zarazem przedostatni rozdział w sposób szczegółowy przedstawia dyskusję zaproponowanego wcześniej modelu matematycznego w postaci układu nieliniowych równań różniczkowych zwyczajnych. Na początku rozdziału przedstawiono rozwiązywalność takiego zagadnienia, następnie opisano zastosowane uproszczenia. W dalszym ciągu zademonstrowano wpływ zastosowanych uproszczeń na kształt analizowanych równań. Dodatkowo podjęto dyskusję o możliwości rozwiązania równań przedstawionych w pracy. Ponadto na podstawie znalezionych przybliżonych rozwiązań wykazano szereg ciekawych własności analizowanego układu równań. Całość została podsumowana celami dalszej pracy oraz syntetycznymi wnioskami, dotyczącymi propozycji innowacyjnej metody sterowania stanami krytycznymi.
Źródło:
Transport Problems; 2013, 8, 4; 137-146
1896-0596
2300-861X
Pojawia się w:
Transport Problems
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Solving linear Fredholm integro-differential equation by Nyström method
Autorzy:
Tair, Boutheina
Guebbai, Hamza
Segni, Sami
Ghiat, Mourad
Powiązania:
https://bibliotekanauki.pl/articles/1839836.pdf
Data publikacji:
2021
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
Fredholm integral equation
system of integral equations
integro-differential equations
Nyström method
równanie całkowe Fredholma
układ równań całkowych
równanie całkowo-różniczkowe
metoda Nyströma
Opis:
The study of the solution’s existence and uniqueness for the linear integro-differential Fredholm equation and the application of the Nyström method to approximate the solution is what we will present in this paper. We use the Neumann theorem to construct a sufficient condition that ensures the solution’s existence and uniqueness of our problem in the Banach space C1 [a,b]. We have applied the Nystrom method based on the trapezoidal ¨ rule to avoid adding other conditions in order to the approximation method’s convergence. The Nyström method discretizes the integro-differential equation into solving a linear system. Only with the existence and uniqueness condition, we show the solution’s existence and uniqueness of the linear system and the convergence of the numerical solution to the exact solution in infinite norm sense. We present two theorems to give a good estimate of the error. Also, to show the efficiency and accuracy of the Nyström method, some numerical examples will be provided at the end of this work.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2021, 20, 3; 53-64
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Steady-state modelling method for matrix-reactance frequency converter with boost topology
Autorzy:
Korotyeyev, I.Ye.
Zięba, B.
Powiązania:
https://bibliotekanauki.pl/articles/140872.pdf
Data publikacji:
2011
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
przekształtnik AC/AC
matrycowo-reaktancyjny przemiennik częstotliwości
metoda Galerkina
równanie różniczkowe
AC/AC converters
matrix-reactance frequency converter
Galerkin's method
extension of differential equations
Opis:
This paper presents a method intended for calculation of steady-state processes in AC/AC three-phase converters that are described by nonstationary periodical differential equations. The method is based on the extension of nonstationary differential equations and the use of Galerkin's method. The results of calculations are presented in the form of a double Fourier series. As an example, a three-phase matrix-reactance frequency converter (MRFC) with boost topology is considered and the results of computation are compared with a numerical method.
Źródło:
Archives of Electrical Engineering; 2011, 60, 2; 137-148
1427-4221
2300-2506
Pojawia się w:
Archives of Electrical Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the semi-analytic technique to deal with nonlinear fractional differential equations
Autorzy:
Khirsariya, Sagar R.
Rao, Snehal B.
Powiązania:
https://bibliotekanauki.pl/articles/2202059.pdf
Data publikacji:
2023
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
fractional differential equation
logistic equation
Fornberg-Whitham equation
homotopy perturbation method
Sawi transform
ułamkowe równanie różniczkowe
równanie logistyczne
równanie Fornberga-Whithama
metoda perturbacji homotopii
Opis:
In this article, we present a novel hybrid approach, by combining the Sawi transform with the homotopy perturbation method, to achieve the approximate and analytic solutions of nonlinear fractional differential equations (ODE as well as PDE) using the time-fractional Caputo derivative. The proposed algorithm is faster and simple compared to other iterative methods. The Sawi transform is used along with the homotopy perturbation method to accelerate the convergence of the series solution. The results discussed using calculations, graphs and tables are compatible for comparison with other known methods like the residual power series method and the exact solution which are discussed in the literature.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2023, 22, 1; 17--30
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
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