Numerical solution of 2D singularly perturbed reaction-diffusion system with multiple scales

摘要

In this article, a robust numerical method is studied to approximate singularly perturbed system of reaction-diffusion problems with multiple scales. The analytical properties of the exact solution have been studied. The numerical method consists of the classical central difference scheme on a Shishkin mesh for spatial semidiscretization processes and the implicit-Euler scheme on a uniform time stepping for temporal derivative. The error estimate is deduced, which exhibits that the numerical approximation is uniformly convergent of almost second-order in spatial variable and first-order in temporal variable. Numerical experiments are given which reveals the effectiveness of the proposed scheme. (C) 2020 Elsevier Ltd. All rights reserved.