Robust computational methods for a coupled system of singularly perturbed reaction-diffusion equations with discontinuous source term

摘要

This paper presents two robust computational methods to solve a system of singularly perturbed weakly coupled reaction-diffusion equations having diffusion parameters with same magnitude with discontinuous source term subject to Dirichlet boundary conditions. On a piecewise-uniform Shishkin mesh, two robust numerical schemes are proposed. Difference scheme-I (DS-I) uses central difference scheme in the inner and outer regions whereas the difference scheme-II (DS-II) is a combination of a central difference scheme and a cubic spline difference scheme used in outer and inner regions respectively. At the point of discontinuity, a five band scheme is used for both the methods. It has been shown that both the proposed computational methods provide almost second order parameter-uniform convergence. Error estimates are derived and numerical results are ensured to support the theory.