Efficient resolution of singularly perturbed coupled systems: Equations of reaction-diffusion

In this communication we consider a class of singularly perturbed linear system of reaction-diffusion type coupled in the reaction terms. To approximate its solution, in [3] J.L. Gracia, F. Lisbona, A uniformly convergent scheme for a system of reaction–diffusion equations, To appear in J. Comp. Appl. Math. the backward Euler method and the central difference scheme on a layer–adapted mesh of Shishkin type was used. We propose a new semi-implicit method which decouples the linear system to be solved at each time level and we prove that it is a uniformly convergent scheme (with respect to the diffusion parameters) in the discrete maximum norm. We display some numerical experiments illustrating in practice the theoretical results. From these examples we can see both the uniform convergence of the numerical method and also its efficiency to approximate the solution of the reaction–diffusion system