Numerical solution for a nonlinear diffusion model with source terms-Reference-Cited by-同舟云学术

Numerical solution for a nonlinear diffusion model with source terms

Published:2023-04-12 Issue:4 Volume:30 Page:539-554
ISSN:1072-947X
Container-title:Georgian Mathematical Journal
language:en
Short-container-title:

Author:

Jangveladze Temur¹,Kiguradze Zurab²,Kratsashvili Maia³,Neta Beny⁴

Affiliation:

1. Ilia Vekua Institute of Applied Mathematics , Ivane Javakhishvili Tbilisi State University , 2 University Str., 0186; and Department of Mathematics, Georgian Technical University, 77 Kostava Ave. , Tbilisi 0175 , Georgia

2. Electromagnetic Compatibility Laboratory , Missouri University of Science and Technology , 4000 Enterprise Drive , Rolla , MO 65409 , USA

3. Rolla Middle School , 1111 Soest Rd , Rolla , MO 65401 , USA

4. Department of Applied Mathematics , Naval Postgraduate School , Monterey , CA 93943 , USA

Abstract

Abstract The nonlinear diffusion system with source terms is studied. This model is derived via Maxwell equations describing electromagnetic field propagation in media. The uniqueness of the solution and its behavior as t → ∞

t\to\infty

are proved. We also prove that the finite difference approximation converges in space and time. Numerical implementation with various experiments for different values of the input parameters is performed to validate the theoretical conclusions.

Funder

Shota Rustaveli National Science Foundation

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/gmj-2023-2016/pdf

Reference28 articles.

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2. translation in Differ. Equ. 48 (2012), no. 1, 72-80.

3. Y. Bai and P. Zhang, On a class of Volterra nonlinear equations of parabolic type, Appl. Math. Comput. 216 (2010), no. 1, 236–240.

4. T. A. Dzhangveladze, The first boundary value problem for a nonlinear equation of parabolic type (in Russian), Dokl. Akad. Nauk SSSR 269 (1983), no. 4, 839-842

5. translation in Soviet Phys. Dokl. 28 (1983), 323-324.

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1. Comparison of several numerical solvers for a discretized nonlinear diffusion model with source terms;Georgian Mathematical Journal;2023-10-27