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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 are
essentially second order convergent uniformly with respect to all of
the parameters
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