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    Wyświetlanie 1-6 z 6
    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:
    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:
    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:
    MHD free convection-radiation interaction in a porous medium - part I: numerical investigation
    Autorzy:
    Vasu, B.
    Gorla, R. S. R.
    Murthy, P. V. S. N.
    Prasad, V. R.
    Bég, O. Anwar
    Siddiqa, S.
    Powiązania:
    https://bibliotekanauki.pl/articles/266199.pdf
    Data publikacji:
    2020
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    pole magnetyczne
    metoda Keller-Box
    nośnik porowaty
    implicit finite difference scheme
    Keller-Box method
    magnetic field
    horizontal circular cylinder
    Opis:
    A numerical investigation of two dimensional steady magnetohydrodynamics heat and mass transfer by laminar free convection from a radiative horizontal circular cylinder in a non-Darcy porous medium is presented by taking into account the Soret/Dufour effects. The boundary layer conservation equations, which are parabolic in nature, are normalized into non-similar form and then solved numerically with the well-tested, efficient, implicit, stable Keller–Box finite-difference scheme. We use simple central difference derivatives and averages at the mid points of net rectangles to get finite difference equations with a second order truncation error. We have conducted a grid sensitivity and time calculation of the solution execution. Numerical results are obtained for the velocity, temperature and concentration distributions, as well as the local skin friction, Nusselt number and Sherwood number for several values of the parameters. The dependency of the thermophysical properties has been discussed on the parameters and shown graphically. The Darcy number accelerates the flow due to a corresponding rise in permeability of the regime and concomitant decrease in Darcian impedance. A comparative study between the previously published and present results in a limiting sense is found in an excellent agreement.
    Źródło:
    International Journal of Applied Mechanics and Engineering; 2020, 25, 1; 198-218
    1734-4492
    2353-9003
    Pojawia się w:
    International Journal of Applied Mechanics and Engineering
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Modelling of heat and flow phenomena occuring in waterwall tubes of boilers for supercritical steam parameters
    Autorzy:
    Zima, W.
    Grądziel, S.
    Cebula, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/240331.pdf
    Data publikacji:
    2010
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    ekran wodny
    model matematyczny
    parametry nadkrytyczne
    parametry rozłożone
    schemat różnicowy
    distributed parameters
    Implicit difference scheme
    mathematical model
    supercritical parameters
    waterwalls
    Opis:
    In this paper a mathematical model enabling the analysis of the heat-flow phenomena occurring in the waterwalls of the combustion chambers of the boilers for supercritical parameters is proposed. It is a one-dimensional model with distributed parameters based on the solution of equations describing the conservation laws of mass, momentum, and energy. The purpose of the numerical calculations is to determine the distributions of the fluid enthalpy and the temperature of the waterwall pipes. This temperature should not exceed the calculation temperature for particular category of steel. The derived differential equations are solved using two methods: with the use of the implicit difference scheme, in which the mesh with regular nodes was applied, and using the Runge-Kutta method. The temperature distribution of the waterwall pipes is determined using the CFD. All thermophysical properties of the fluid and waterwall pipes are computed in real-time. The time-spatial heat transfer coefficient distribution is also computed in the on-line mode. The heat calculations for the combustion chamber are carried out with the use of the zone method, thus the thermal load distribution of the waterwalls is known. The time needed for the computations is of great importance when taking into consideration calculations carried out in the on-line mode. A correctly solved one-dimensional model ensures the appropriately short computational time.
    Źródło:
    Archives of Thermodynamics; 2010, 31, 3; 19-31
    1231-0956
    2083-6023
    Pojawia się w:
    Archives of Thermodynamics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-6 z 6

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