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Wyświetlanie 1-15 z 119
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:
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:
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:
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:
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:
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:
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:
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:
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:
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:
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:
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:
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:
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
Wyświetlanie 1-15 z 119

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