Second Order Uniformly Convergent Numerical Method for a Coupled System of Singularly Perturbed Reaction-Diffusion Problems with Discontinuous Source Term

In this work we consider a coupled system of m(>= 2) linear singularly perturbed equations of reaction-diffusion type coupled in the reaction terms with discontinuous source term. The leading term of each equation is multiplied by a small positive parameter. These singular perturbation parameters are assumed to be distinct in magnitude. Overlapping boundary and interior layers can appear in the solution. A numerical method is constructed that involve an appropriate piecewise-uniform Shishkin mesh, which is fitted to both the boundary and interior layers. The parameter-uniform convergence of the numerical approximations is examined.