Second Order Uniform Approximations for the Solution of Time Dependent Singularly Perturbed Reaction-Diffusion Systems

Abstract

In this work we consider a parabolic system of two linear singularly perturbed equations of reaction-diffusion type coupled in the reaction terms. To obtain an efficient approximation of the exact solution we propose a numerical method combining the Crank-Nicolson method used in conjunction with the central finite difference scheme defined on a piecewise uniform Shishkin mesh. The method gives uniform numerical approximations of second order in time and almost second order in space. Some numerical experiments are given to support the theoretical results.