Efficient uniformly convergent numerical methods for singularly perturbed parabolic reaction–diffusion systems with discontinuous source term

Abstract

[EN] This article is concerned with the construction and analysis of efficient uniformly convergent methods for a class of parabolic systems of coupled singularly perturbed reaction–diffusion problems with discontinuous source term. Due to the discontinuity in the source term, the solution to this problem exhibits interior layers along with boundary layers, which are overlapping and interacting in nature. To achieve an efficient numerical solution for the coupled system under consideration, at interior points (excluding the interface point) we employ a special finite difference scheme in time (where the components of the approximate solution are decoupled at each time level) and the central difference scheme in space; for mesh points on the interface, a special finite difference scheme decoupling the components of the approximate solution is developed. A rigorous error analysis is provided, establishing the method’s uniform convergence. In terms of computational cost, our numerical methods are more efficient than existing approaches for solving this class of problems. Finally, we provide numerical results to substantiate the theory and showcase the efficiency of our methods.