A computational approach for a two-parameter singularly perturbed system of partial differential equations with discontinuous coefficients

This work aims at obtaining a numerical approximation to the solution of a two-parameter singularly perturbed convection-diffusion-reaction system of partial differential equations with discontinuous coefficients. This discontinuity, together with small values of the perturbation parameters, causes interior and boundary layers to appear in the solution. To obtain appropriate point-wise accuracy, we have considered a central finite-difference approach in the space variable which is defined on a piecewise uniform Shishkin mesh and an implicit Euler scheme in the temporal variable defined on a uniform mesh. Some computational experiments have been performed, which confirm the theoretical findings.