AN EFFICIENT NUMERICAL METHOD FOR A SYSTEM OF SINGULARLY PERTURBED REACTION-DIFFUSION EQUATIONS

摘要

Often, when singularly perturbed problems are solved on non-uniform meshes, solutions are decomposed into their regular and singular components. The analysis of the underlying method is conducted accordingly. In this paper, we consider a system of two coupled singularly perturbed reaction-diffusion equations. This type of systems are encountered in various fields of applied science such as chemical kinetics and predator-prey population dynamics. The presence of a small positive parameter multiplying the highest derivative in each equation leads to two overlapping and interacting boundary layers. We propose a fitted operator finite difference method to solve such systems. We show that the fitted operator satisfies a maximum principle. A rigorous error analysis (without decomposition of the solution) shows that the method is second order uniformly convergent. The theoretical results are confirmed through computational investigations.