A singularly perturbed linear system of second order ordinary differential
equations of reaction-diffusion type with given boundary conditions is
considered. The leading term of each equation is multiplied by a small positive
parameter. These singular perturbation parameters are assumed to be distinct.
The components of the solution exhibit overlapping layers. Shishkin
piecewise-uniform meshes are introduced, which are used in conjunction with a
classical finite difference discretisation, to construct a numerical method for
solving this problem. It is proved that the numerical approximations obtained
with this method is essentially second order convergent uniformly with respect
to all of the parameters
