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