A non-uniform difference scheme for solving singularly perturbed 1D-parabolic reaction-convection-diffusion systems with two small parameters and discontinuous source terms

This paper aims at solving numerically the 1-D weakly coupled system of singularly perturbed reaction-convection-diffusion partial differential equations with two small parameters and discontinuous source terms. Boundary and interior layers appear in the solutions of the problem for sufficiently small values of the perturbation parameters. A numerical algorithm based on finite difference operators and an appropriate piecewise uniform mesh is constructed and its characteristics are analyzed. The method is confirmed to reach almost first order convergence, independently of the values of the perturbation parameters. Some numerical experiments are presented, which serve to illustrate the theoretical results.