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Tytuł:
An interval difference method for solving the wave equation
Autorzy:
Szyszka, B.
Powiązania:
https://bibliotekanauki.pl/articles/378277.pdf
Data publikacji:
2012
Wydawca:
Politechnika Poznańska. Wydawnictwo Politechniki Poznańskiej
Tematy:
wave equation
difference interval method
interval method
floating point interval arithmetic
Opis:
In the paper a difference interval method for solving the wave equation together the initial-boundary value problems is presented. Using an interval method together floating-point interval arithmetic guarantee, that obtained interval solutions contain all numerical errors. Additionally, each exact solution is included into interval solution. In numerical experiments it is guarantee contain all numerical errors in obtained interval solutions. Taken into consideration is the central discretization method with regard to space and time. An initial condition is approximated by the third-order Taylor polynomial with local truncation error of order 0(h4). In the paper new formula, which described discretization of the initial condition, is proposed. Therefore more exact solutions are obtained then in the previous considerations.
Źródło:
Poznan University of Technology Academic Journals. Electrical Engineering; 2012, 69; 161-168
1897-0737
Pojawia się w:
Poznan University of Technology Academic Journals. Electrical Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Water absorption of black chickpea using a finite difference method
Autorzy:
Dibagar, Nesa
Kowalski, Stefan Jan
Chayjan, Reza Amiri
Powiązania:
https://bibliotekanauki.pl/articles/185088.pdf
Data publikacji:
2019
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
water absorption
black chickpea
finite difference method
Peleg’s model
absorpcja wody
czarna ciecierzyca
metoda różnic skończonych
Model Pelega
Opis:
Evaluation of moisture absorption in foodstuffs such as black chickpea is an important stage for skinning and cropping practices. Water uptake process of black chickpea was discussed through normal soaking in four temperature levels of 20, 35, 50 and 65 °C for 18 hours, and then the hydration kinetics was predicted by Peleg’s model and finite difference strategy. Model results showed that with increasing soaking temperature from 20 to 65 °C, Peleg’s rate and Peleg’s capacity constant reduced from 13.368×10-2 to 5.664×10-2 and 9.231×10-3 to 9.138×10-3, respectively. Based on key results, a rise in the medium temperature caused an increase in the diffusion coefficient from 5.24×10-10 m2/s to 4.36×10-9 m2/s, as well. Modelling of moisture absorption of black chickpea was also performed employing finite difference strategy. Comparing the experimental results with those obtained from the analytical solution of the theoretical models revealed a good agreement between predicted and experimental data. Peleg’s model and finite difference technique revealed their predictive function the best at the temperature of 65 °C.
Źródło:
Chemical and Process Engineering; 2019, 40, 3; 327--341
0208-6425
2300-1925
Pojawia się w:
Chemical and Process Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Mathematical modeling of air duct heater using the finite difference method
Autorzy:
Sarafraz M., M.
Peyghambarzadeh S., M.
Marahel, A.
Powiązania:
https://bibliotekanauki.pl/articles/779839.pdf
Data publikacji:
2011
Wydawca:
Zachodniopomorski Uniwersytet Technologiczny w Szczecinie. Wydawnictwo Uczelniane ZUT w Szczecinie
Tematy:
nagrzewnica kanałowa
modelowanie
zmienne właściwości fizyczne
różnice skończone
logarytm średniej temperatury
duct heater
modeling
variable physical properties
finite differences
log mean temperature difference
Opis:
In this research, mathematical modeling of a duct heater has been performed using energy conservation law, Stefan-Boltzman law in thermal radiation, Fourier’s law in conduction heat transfer, and Newton’s law of cooling in convection heat transfer. The duct was divided to some elements with equal length. Each element has been studied separately and air physical properties in each element have been used based on its temperature. The derived equations have been solved using the finite difference method and consequently air temperature, internal and external temperatures of the wall, internal and external convection heat transfer coeffi cients, and the quantity of heat transferred have been calculated in each element and effects of the variation of heat transfer parameters have been surveyed. The results of modelling presented in this paper can be used for the design and optimization of heat exchangers.
Źródło:
Polish Journal of Chemical Technology; 2011, 13, 4; 47-52
1509-8117
1899-4741
Pojawia się w:
Polish Journal of Chemical Technology
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Synteza układów odwracalnych metodą różnicową
Difference method of reversible circuits synthesis
Autorzy:
Skorupski, A.
Pawłowski, M.
Gracki, K.
Kerntopf, P.
Powiązania:
https://bibliotekanauki.pl/articles/152913.pdf
Data publikacji:
2013
Wydawca:
Stowarzyszenie Inżynierów i Techników Mechaników Polskich
Tematy:
odwracalne układy logiczne
projektowanie układów
reversible logic circuits
circuit synthesis
Opis:
W niniejszej pracy przedstawiony jest prosty algorytm projektowania układów odwracalnych. Proponowany algorytm polega na wyznaczeniu dla danej funkcji zbioru bramek (nazywanego zbiorem bramek pierwszych), które mogą znajdować się na początku układu kaskadowego realizującego zadaną funkcję. Po wyznaczeniu takiego zbioru można wybrać jeden z jego elementów, a następnie powtórzyć algorytm dla tzw. funkcji resz-towej. Postępuje się tak, aż do momentu, gdy funkcja resztowa stanie się funkcją identycznościową. Liczba iteracji algorytmu jest równa liczbie bramek projektowanej kaskady.
Research on reversible logic circuits is motivated by advances in quantum computing, nanotechnology and low-power design. Im-plementation of such functions is realized by special gates. These gates always form a cascade circuit. Minimization of such circuits is a very difficult problem. In this paper a novel concept of synthesis of reversible logic is presented. For simplicity, the method is described for three variables only but it is scalable for more variables. The proposed method is based on XOR function applied to input and output sides of the truth table of a function to be synthesized. The result of applying XOR function indicates bits in the truth table which have to be changed by reversible gates. Due to this property the number of analyzed gates is small. We present the comparison of three variants of the difference method. Each of them leads to different numbers of 3-variable functions for which exact optimal circuits have been found.
Źródło:
Pomiary Automatyka Kontrola; 2013, R. 59, nr 8, 8; 784-786
0032-4140
Pojawia się w:
Pomiary Automatyka Kontrola
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Application of finite difference method for measurement simulation in ultrasound transmission tomography
Autorzy:
Kania, Konrad
Mazurek, Mariusz
Rymarczyk, Tomasz
Powiązania:
https://bibliotekanauki.pl/articles/2097434.pdf
Data publikacji:
2022
Wydawca:
Polskie Towarzystwo Promocji Wiedzy
Tematy:
forward problem
ultrasound transmission tomography
sensors
machine learning
finite difference
Opis:
In this work, we present a computer simulation model that generates the propagation of sound waves to solve a forward problem in ultrasound transmission tomography. The simulator can be used to create data sets used in the supervised learning process. A solution to the "free-space" boundary problem was proposed, and the memory consumption was significantly optimized from O(n2) to O(n). The given method of simulating wave scattering enables the control of the noise extinction time within the tomographic probe and the permeability of the sound wave. The presented version of the script simulates the classic variant of a circular probe with evenly distributed sensors around the circumference.
Źródło:
Applied Computer Science; 2022, 18, 2; 101--109
1895-3735
Pojawia się w:
Applied Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Finite difference method for the fractional order pseudo telegraph integro-differential equation
Autorzy:
Modanli, Mahmut
Ozbag, Fatih
Akgül, Ali
Powiązania:
https://bibliotekanauki.pl/articles/2175509.pdf
Data publikacji:
2022
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
pseudo telegraph equation
integro-differential equation
finite difference scheme
stability analysis
równanie całkowo-różniczkowe
metoda różnic skończonych
analiza stabilności
Opis:
The main goal of this paper is to investigate the numerical solution of the fractional order pseudo telegraph integro-differential equation. We establish the first order finite difference scheme. Then for the stability analysis of the constructed difference scheme, we give theoretical statements and prove them. We also support our theoretical statements by performing numerical experiments for some fractions of order α.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2022, 21, 1; 41--54
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
An extended finite difference method for singular perturbation problems on a non-uniform mesh
Autorzy:
Swarnakar, D.
Kumar, V. Ganesh
Soujanya, G. B. S. L.
Powiązania:
https://bibliotekanauki.pl/articles/2174215.pdf
Data publikacji:
2022
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
siatka niejednorodna
metoda różnic skończonych
warstwa graniczna
non uniform grid
finite difference method
singular perturbation
boundary layer
Opis:
An extended second order finite difference method on a variable mesh is proposed for the solution of a singularly perturbed boundary value problem. A discrete equation is achieved on the non uniform mesh by extending the first and second order derivatives to the higher order finite differences. This equation is solved efficiently using a tridiagonal solver. The proposed method is analysed for convergence, and second order convergence is derived. Model examples are solved by the proposed scheme and compared with available methods in the literature to uphold the method.
Źródło:
International Journal of Applied Mechanics and Engineering; 2022, 27, 1; 203--214
1734-4492
2353-9003
Pojawia się w:
International Journal of Applied Mechanics and Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Difference method for a nonlinear parabolic equation of second order in two space variables
Autorzy:
Kawecki, Roman
Powiązania:
https://bibliotekanauki.pl/articles/747916.pdf
Data publikacji:
1990
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
Finite difference methods
Stability and convergence of numerical methods
Opis:
.
A.C. Reynolds in his paper (1972) proposed a difference parametric method for solving the Fourier problem for a nonlinear parabolic equation of second order in one space variable. The paper presents a generalization of Reynolds’ method for the problem in two space variables with mixed derivatives. In this paper, Fourier problems for a general class of nonlinear parabolic equation, in QT = Q x [0, T], are studied. To solve this problem we construct a finite difference scheme with a real parameter. We prove that the solutions of certain associated finite difference equations are unique and converge to the solution of the initial-boundary value problem with 0(h^2) rate of convergence.
Źródło:
Mathematica Applicanda; 1990, 18, 32
1730-2668
2299-4009
Pojawia się w:
Mathematica Applicanda
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Implicit scheme of the finite difference method for 1D dual-phase lag equation
Autorzy:
Majchrzak, E.
Mochnacki, B.
Powiązania:
https://bibliotekanauki.pl/articles/973620.pdf
Data publikacji:
2017
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
micro-scale heat conduction
dual-phase lag equation
finite difference method
stability of FDM implicit scheme
równanie z dwoma czasami opóźnień
metoda różnic skończonych
DPLE
schemat FDM
Opis:
The 1D dual-phase lag equation (DPLE) is solved using the implicit FDM scheme. The dual phase lag equation is the hyperbolic PDE and contains a second order time derivative and higher order mixed derivative in both time and space. The DPLE results from the generalization of the well known Fourier law in which the delay times are taken into account. So, in the equation discussed, two positive parameters appear. They correspond to the relaxation time τq and the thermalization time τ T. The DPLE finds, among others, the application as the mathematical description of the thermal processes proceeding in the micro-scale. In the paper, the numerical solution of DPLE based on the implicit scheme of the FDM is presented. The authors show that a such an approach in the case of DPLE leads to the unconditionally stable differential scheme.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2017, 16, 3; 37-46
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Implicit scheme of the finite difference method for the second-order dual phase lag equation
Autorzy:
Majchrzak, E.
Mochnacki, B.
Powiązania:
https://bibliotekanauki.pl/articles/280549.pdf
Data publikacji:
2018
Wydawca:
Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
Tematy:
microscale heat transfer
dual phase lag model
implicit scheme of finite difference method
Opis:
The second-order dual phase lag equation (DPLE) as a mathematical model of the microscale heat transfer is considered. It is known that the starting point determining the final form of this equation is the generalized Fourier law in which two positive constants (the relaxation and thermalization times) appear. Depending on the order of the generalized Fourier law expansion into the Taylor series, different forms of the DPLE can be obtained. As an example of the problem described by the second-order DPLE equation, thermal processes proceeding in the domain of a thin metal film subjected to a laser pulse are considered. The numerical algorithm is based on an implicit scheme of the finite difference method. At the stage of numerical modeling, the first, second and mixed order of the dual phase lag equation are considered. In the final part of the paper, examples of different solutions are presented and conclusions are formulated.
Źródło:
Journal of Theoretical and Applied Mechanics; 2018, 56, 2; 393-402
1429-2955
Pojawia się w:
Journal of Theoretical and Applied Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Influence of discrete model parameters on the KZK equation solution using the finite difference method
Autorzy:
Baranowska, A.
Powiązania:
https://bibliotekanauki.pl/articles/332604.pdf
Data publikacji:
1997
Wydawca:
Polskie Towarzystwo Akustyczne
Opis:
Khokhlov - Zabolotskaya - Kuznetsov (KZK) nonlinear parabolic wave equation describes the acoustic pressure changes in the nonlinear and dissipative medium along the sound beam. This equation is solving numerically. On the basis of the finite difference method computer programs have been worked out. These programs allow to conduct different numerical investigations. The paper presents a mathematical model of finite amplitude wave propagation problem. The results of numerical investigations refer to influence of discrete model parameters on accuracy of numerical calculations are studied.
Źródło:
Hydroacoustics; 1997, 1; 59-64
1642-1817
Pojawia się w:
Hydroacoustics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The finite difference method in the 2D Fourier equation with Robin’s boundary condition
Autorzy:
Biernat, G.
Lara-Dziembek, S.
Pawlak, E.
Powiązania:
https://bibliotekanauki.pl/articles/122782.pdf
Data publikacji:
2013
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
block matrices
n-band matrices
determinant
Fourier equation
boundary condition
Opis:
This paper contains the application of the Finite Difference Method in the two-dimensional Fourier equation using Robin’s boundary condition (the third boundary condition).
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2013, 12, 4; 5-11
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
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:
Elastic critical moment for bisymmetric steel profiles and its sensitivity by the finite difference method
Autorzy:
Kamiński, M.
Supeł, Ł.
Powiązania:
https://bibliotekanauki.pl/articles/265535.pdf
Data publikacji:
2016
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
moment krytyczny
konstrukcja murowana
metoda elementów skończonych
critical moment
finite difference method
sensitivity analysis
thin walled structures
finite element method
Opis:
It is widely known that lateral-torsional buckling of a member under bending and warping restraints of its cross-sections in the steel structures are crucial for estimation of their safety and durability. Although engineering codes for steel and aluminum structures support the designer with the additional analytical expressions depending even on the boundary conditions and internal forces diagrams, one may apply alternatively the traditional Finite Element or Finite Difference Methods (FEM, FDM) to determine the so-called critical moment representing this phenomenon. The principal purpose of this work is to compare three different ways of determination of critical moment, also in the context of structural sensitivity analysis with respect to the structural element length. Sensitivity gradients are determined by the use of both analytical and the central finite difference scheme here and contrasted also for analytical, FEM as well as FDM approaches. Computational study is provided for the entire family of the steel I- and H - beams available for the practitioners in this area, and is a basis for further stochastic reliability analysis as well as durability prediction including possible corrosion progress.
Źródło:
International Journal of Applied Mechanics and Engineering; 2016, 21, 1; 37-59
1734-4492
2353-9003
Pojawia się w:
International Journal of Applied Mechanics and Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
An unconditionally stable nonstandard finite difference method applied to a mathematical model of HIV infection
Autorzy:
Obaid, H. A.
Ouifki, R.
Patidar, K. C.
Powiązania:
https://bibliotekanauki.pl/articles/331053.pdf
Data publikacji:
2013
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
HIV infection
dynamical system
nonstandard finite difference methods
equilibria
stability
zakażenie HIV
układ dynamiczny
metoda różnic skończonych
równowaga
Opis:
We formulate and analyze an unconditionally stable nonstandard finite difference method for a mathematical model of HIV transmission dynamics. The dynamics of this model are studied using the qualitative theory of dynamical systems. These qualitative features of the continuous model are preserved by the numerical method that we propose in this paper. This method also preserves the positivity of the solution, which is one of the essential requirements when modeling epidemic diseases. Robust numerical results confirming theoretical investigations are provided. Comparisons are also made with the other conventional approaches that are routinely used for such problems.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2013, 23, 2; 357-372
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The n-dimensional Fourier equation with the Robins boundary condition using the finite difference method
Autorzy:
Biernat, G.
Lara-Dziembek, S.
Pawlak, E.
Powiązania:
https://bibliotekanauki.pl/articles/122283.pdf
Data publikacji:
2014
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
block matrices
determinant
Fourier equation
boundary condition
macierze blokowe
determinanta
równanie Fouriera
warunek brzegowy
Opis:
The article is a continuation of the considerations on the three-dimensional Fourier equation supplemented by the third boundary condition (the Robin’s condition). The paper is based on the Finite Difference Method.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2014, 13, 3; 13-20
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The 3D Fourier equation with the Robin’s boundary condition using the finite difference method
Autorzy:
Biernat, G.
Lara-Dziembek, S.
Pawlak, E.
Powiązania:
https://bibliotekanauki.pl/articles/123013.pdf
Data publikacji:
2014
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
block matrices
determinant
Fourier equation
boundary condition
macierze blokowe
determinanta
równanie Fouriera
warunek brzegowy
Opis:
This article is a continuation of the discussion on the two-dimensional Fourier equation with Robin’s boundary condition. In the paper the Finite Difference Method is applied.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2014, 13, 1; 5-11
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-25 z 173

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