The Convergence of a Finite Difference Method on Layer-Adapted Mesh for a Singularly Perturbed System

Abstract

This paper is concerned with the numerical solution for singular perturbation system of two coupled ordinary differential equations with first and second orders and with initial and boundary conditions, respectively. Finite difference scheme on a special non-uniform mesh, whose solution converges pointwise independently of the singular perturbation parameter is constructed and analyzed. Numerical results supporting the theory are presented. (C) 2004 Elsevier Inc. All rights reserved.