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Wyświetlanie 1-15 z 31
Tytuł:
Heat flux formulation for 1D dual-phase lag equation
Autorzy:
Majchrzak, E.
Kałuża, G.
Powiązania:
https://bibliotekanauki.pl/articles/122784.pdf
Data publikacji:
2015
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
dual phase lag equation
finite difference method
thin metal film
Opis:
The thin metal film subjected to the ultra-short laser pulse is analyzed. Heat transfer processes occurring in the domain considered are described by the dual-phase lag model in which the unknown is the heat flux, not, as usual, temperature. This approach is especially convenient in the case of Neumann boundary conditions, which are taken into account here. The mathematical model supplemented by initial conditions is solved using the explicit scheme of finite difference method. In the final part of the paper the examples of computations are shown and the conclusions are formulated.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2015, 14, 1; 71-78
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A new numerical scheme for solving the two dimensional fractional diffusion equation
Autorzy:
Dilara, Altan Koç
Mustafa, Gülsu
Powiązania:
https://bibliotekanauki.pl/articles/1839848.pdf
Data publikacji:
2021
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
finite difference method
fractional calculus
numerical methods
metoda różnic skończonych
rachunek ułamkowy
metody numeryczne
Opis:
In this study, the locally one dimensional (LOD) method is used to solve the two dimensional time fractional diffusion equation. The fractional derivative is the Caputo fractional derivative of order α. The rate of convergence of the finite difference method is presented. It is seen that this method is in agreement with the obtained numerical solutions with acceptable central processing unit time (CPU time). Error estimates, numerical and exact results are tabulated. The graphics of errors are given.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2021, 20, 1; 5-16
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A numerical scheme for time-fractional fourth-order reaction-diffusion model
Autorzy:
Koç, Dilara Altan
Powiązania:
https://bibliotekanauki.pl/articles/24201500.pdf
Data publikacji:
2023
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
implicit finite difference method
fractional calculus
diffusion equation
niejawna metoda różnic skończonych
rachunek ułamkowy
równanie dyfuzji
Opis:
In fractional calculus, the fractional differential equation is physically and theoretically important. In this article an efficient numerical process has been developed. Numerical solutions of the time fractional fourth order reaction diffusion equation in the sense of Caputo derivative is obtained by using the implicit method, which is a finite difference method and is developed by increasing the number of iterations. The advantage of the implicit difference scheme is unconditionally stable. The stability analysis and convergency have been proven. A numerical example has been presented, and the validity of the method is supported by tables and graphics.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2023, 22, 2; 15--25
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Analysis of ultrashort laser pulse interactions with metal films using a two-temperature model
Autorzy:
Majchrzak, E.
Dziatkiewicz, J.
Powiązania:
https://bibliotekanauki.pl/articles/122931.pdf
Data publikacji:
2015
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
microscale heat transfer
two-temperature model
finite difference method
mikroskalowy przepływ ciepła
dwu-temperaturowy model
metoda różnic skończonych
Opis:
In the paper the problem of thin metal film subjected to the action of the high laser fluence and the ultrashort pulse width is considered. The mathematical model consists of the equations describing the electrons and phonons temperatures and the relationships between the heat fluxes and temperature gradients of electrons and phonons. The problem is solved using the explicit scheme of the finite difference method with staggered grid. In the final part the results of computations and conclusions are presented.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2015, 14, 2; 31-39
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Numerical scheme for one phase 1D fractional Stefan problem using the similarity variable technique
Autorzy:
Błasik, M.
Powiązania:
https://bibliotekanauki.pl/articles/122307.pdf
Data publikacji:
2014
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
Stefan problem
anomalous diffusion
fractional derivative
finite difference method
zagadnienie Stefana
dyfuzja anomalna
pochodna ułamkowa
metoda różnic skończonych
Opis:
In this paper we present a numerical method to solve a one-dimensional, one-phase extended Stefan problem with fractional time derivative described in the Caputo sense. The proposed method is based on applying a similarity variable for the anomalous-diffusion equation and the finite difference method. In the final part, examples of numerical results are discussed.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2014, 13, 1; 13-21
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Bioheat transfer equation : the problem of FDM explicit scheme stability
Autorzy:
Tuzikiewicz, W.
Duda, M.
Powiązania:
https://bibliotekanauki.pl/articles/122648.pdf
Data publikacji:
2015
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
bio-heat transfer
finite difference method
stability condition
von Neumann method
wymiana biociepła
metoda różnic skończonych
stan stateczności
Opis:
In the paper the problem of explicit FDM scheme stability for the bio-heat transfer equation (the Pennes equation) is discussed. To formulate the appropriate condition the von Neumann approach is applied. The first chapter contains the known derivation of FDM stability condition for the Fourier equation. In the second part, a similar condition is found for the case of the bio-heat transfer equation containing both the perfusion and metabolic heat sources.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2015, 14, 4; 139-144
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Effects of the porous boundary and inclined magnetic field on MHD flow in a rectangular duct
Autorzy:
Chutia, Muhim
Powiązania:
https://bibliotekanauki.pl/articles/1839735.pdf
Data publikacji:
2020
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
MHD
rectangular duct
porous boundary
inclined magnetic field
finite difference method
kanał prostokątny
ułamkowe równanie różniczkowe
pochodna ułamkowa
Opis:
In this work, a steady two dimensional MHD flow of a viscous incompressible fluid through a rectangular duct under the action of an inclined magnetic field with a porous boundary has been investigated. The coupled partial differential equations are transformed into a system of algebraic equations using the finite difference method and are then solved simultaneously using the Gauss Seidal iteration method by programming in Matlab software. Numerical solutions for velocity, induced magnetic field and current density lines are obtained and analyzed for different values of dimensionless parameters namely suction/injection parameter (S), Hartmann number (M) and inclination angle (θ) and are presented graphically.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2020, 19, 4; 33-44
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Effects of the porous boundary and inclined magnetic field on MHD flow in a rectangular duct
Autorzy:
Chutia, Muhim
Powiązania:
https://bibliotekanauki.pl/articles/1839745.pdf
Data publikacji:
2020
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
MHD
rectangular duct
porous boundary
inclined magnetic field
finite difference method
kanał prostokątny
ułamkowe równanie różniczkowe
pochodna ułamkowa
Opis:
In this work, a steady two dimensional MHD flow of a viscous incompressible fluid through a rectangular duct under the action of an inclined magnetic field with a porous boundary has been investigated. The coupled partial differential equations are transformed into a system of algebraic equations using the finite difference method and are then solved simultaneously using the Gauss Seidal iteration method by programming in Matlab software. Numerical solutions for velocity, induced magnetic field and current density lines are obtained and analyzed for different values of dimensionless parameters namely suction/injection parameter (S), Hartmann number (M) and inclination angle (θ) and are presented graphically.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2020, 19, 4; 33-44
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
1D generalized dual-phase lag equation. Sensitivity analysis with respect to the porosity
Autorzy:
Kałuża, G.
Majchrzak, E.
Turchan, Ł.
Powiązania:
https://bibliotekanauki.pl/articles/123000.pdf
Data publikacji:
2016
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
bioheat transfer
generalized dual-phase lag model
sensitivity analysis
finite difference method
przepływ biociepła
metoda różnic skończonych
analiza wrażliwości
Opis:
Thermal processes occurring in the heated tissue are described by the 1D generalized dual-phase lag equation supplemented by appropriate boundary and initial conditions. Using the sensitivity analysis method, the additional problem connected with the porosity is formulated. Both problems are solved by means of the explicit scheme of the finite difference method. In this way it is possible to estimate the temperature changes due to the perturbation of porosity. In the final part of the paper, the example of computation is shown and the conclusions are formulated.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2016, 15, 1; 49-58
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Implicit solution of 1d nonlinear porous medium equation using the four-point Newton- EGMSOR iterative method
Autorzy:
Chew, J. V. L.
Sulaiman, J.
Powiązania:
https://bibliotekanauki.pl/articles/122819.pdf
Data publikacji:
2016
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
porous medium equation
finite difference scheme
Newton method
Explicit Group
MSOR
równania różniczkowe cząstkowe
metoda różnic skończonych
metoda Newtona
Opis:
The numerical method can be a good choice in solving nonlinear partial differential equations (PDEs) due to the difficulty in finding the analytical solution. Porous medium equation (PME) is one of the nonlinear PDEs which exists in many realistic problems. This paper proposes a four-point Newton-EGMSOR (4-Newton-EGMSOR) iterative method in solving 1D nonlinear PMEs. The reliability of the 4-Newton-EGMSOR iterative method in computing approximate solutions for several selected PME problems is shown with comparison to 4-Newton-EGSOR, 4-Newton-EG and Newton-Gauss-Seidel methods. Numerical results showed that the proposed method is superior in terms of the number of iterations and computational time compared to the other three tested iterative methods.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2016, 15, 2; 11-21
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
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:
Numerical analysis of biological tissue heating using the dual-phase lag equation with temperature – dependent parameters
Autorzy:
Majchrzak, Ewa
Stryczyński, Mikołaj
Powiązania:
https://bibliotekanauki.pl/articles/2202034.pdf
Data publikacji:
2022
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
bioheat transfer
dual-phase lag model
temperature-dependent parameter
finite difference method
przepływ biociepła
model dwufazowego opóźnienia
metoda różnic skończonych
Opis:
The dual-phase lag equation is formulated for the case when the thermophysical parameters occurring in this equation are temperature-dependent. The axial-symmetrical domain of biological tissue heated by an external heat source is considered. The problem is solved using the implicit scheme of the finite difference method. At the stage of numerical computations, the analytical relationships taken from the literature describing changes in parameters are taken into account.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2022, 21, 3; 85--98
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The finite difference method on adaptive mesh for singularly perturbed nonlinear 1D reaction diffusion boundary value problems
Autorzy:
Duru, Hakkı
Güneş, Baransel
Powiązania:
https://bibliotekanauki.pl/articles/1839748.pdf
Data publikacji:
2020
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
boundary value problem
singularly perturbed problem
finite difference method
metoda różnic skończonych
schemat różnicowy
metoda Newtona-Raphsona
równanie reakcji–dyfuzji
Opis:
In this paper, we study singularly perturbed nonlinear reaction-diffusion equations. The asymptotic behavior of the solution is examined. The difference scheme which is accomplished by the method of integral identities with using of interpolation quadrature rules with weight functions and remainder term integral form is established on adaptive mesh. Uniform convergence and stability of the difference method are discussed in the discrete maximum norm. The discrete scheme shows that orders of convergent rates are close to 2. An algorithm is presented, and some problems are solved to validate the theoretical results.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2020, 19, 4; 45-56
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Dual-phase lag equation. Stability conditions of a numerical algorithm based on the explicit scheme of the finite difference method
Autorzy:
Majchrzak, E.
Mochnacki, B.
Powiązania:
https://bibliotekanauki.pl/articles/122742.pdf
Data publikacji:
2016
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
heat conduction
dual-phase lag equation
finite difference method
stability conditions of FDM explicit scheme
przewodzenie ciepła
metoda różnic skończonych
Opis:
The dual-phase lag equation (DPLE) is considered. This equation belongs to the group of hyperbolic PDE, contains a second order time derivative and higher order mixed derivative in both time and space. From the engineer’s point of view, the DPLE results from the generalized form of the Fourier law. It is applied as a mathematical model of thermal processes proceeding in the micro-scale and also in the case of bio-heat transfer problem analysis. At the stage of numerical computations the different approximate methods of the PDE solving can be used. In this paper, the authors present the considerations concerning the stability conditions of the explicit scheme of finite difference method (FDM). The appropriate conditions have been found using the von Neumann analysis. In the final part of the paper, the results of testing computations are shown.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2016, 15, 3; 89-96
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Lie symmetries and conserved quantities of discrete constrained Hamilton systems
Autorzy:
Mingliang, Z.
Powiązania:
https://bibliotekanauki.pl/articles/122848.pdf
Data publikacji:
2018
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
discrete difference variational principle
constrained Hamilton systems
Lie symmetries
conserved quantities
symetrie Liego
system Hamiltona
teoria symetrii
dyskretne uklady mechaniczne
Opis:
In this paper, the Lie symmetry theory of discrete singular systems is studied in phase space. Firstly, the discrete canonical equations and the energy evolution equations of the constrained Hamilton systems are established based on the discrete difference variational principle. Secondly, the Lie point transformation of discrete group is applied to the difference equations and constraint restriction, and the Lie symmetry determination equations of the discrete constrained Hamilton systems are obtained; Meanwhile, the Lie symmetries of singular systems lead to the discrete Noehter type conserved quantities when the structure condition equations (discrete Noether identity) are established. Finally,an example is given to illustrate the application, the results show that the conservative constrained Hamilton systems also have the discrete energy conservation.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2018, 17, 3; 61-70
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 31

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