A finite-difference scheme for a coupled system of singularly perturbed time-dependent reaction–diffusion equations with discontinuous source terms

Abstract

[EN]In this paper, a coupled system of singularly perturbed parabolic one dimensional reaction–diffusion equations with discontinuous source terms is considered. To obtain a reliable approximation of the system solution, we construct a numerical method by using an effective finite difference scheme which involves a suitable layer-adapted piece-wise uniform Shishkin mesh. We show that the approximations provided by the proposed numerical method converge uniformly with respect to the singular perturbation parameter. The performance of the singularly perturbed parabolic system successfully tested illustrates the agreement with the theoretical results.