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In this paper, a boundary value problem for a singularly perturbed linearsystem of two second order ordinary differential equations of convection-diffusion type is considered on the interval [0, 1]. The components of thesolution of this system exhibit boundary layers at 0. A numerical methodcomposed of an upwind finite difference scheme applied on a piecewise uniformShishkin mesh is suggested to solve the problem. The method is proved to befirst order convergent in the maximum norm uniformly in the perturbationparameters. Numerical examples are provided in support of the theory.

A parameter uniform fitted mesh method for a weakly coupled system of two singularly perturbed convection-diffusion equations