Pre-publicaciones Del Seminario Matematico 2008 an Almost Second Order Uniformly Convergent Method for Parabolic Singularly Perturbed Reaction- Diffusion Systems an Almost Second Order Uniformly Convergent Method for Parabolic Singularly Perturbed Reaction-diffusion Systems *

In this work we consider a parabolic system of two linear singularly perturbed equations of reaction-diffusion type coupled in the reaction terms. The small values of the diffusion parameters, in general, cause that the solution has boundary layers at the ends of the spatial domain. To obtain an efficient approximation of the solution we propose a numerical method combining the Crank-Nicolson method joint to the central finite difference scheme defined on a piecewise uniform Shishkin mesh. The resulting method is uniformly convergent of second order in time and almost second order in space, if the discretization parameters satisfy a non restrictive relation. We display some numerical experiments showing the order of uniform convergence theoretically proved. These numerical results also indicate that the relation between the discretization parameters is not necessary in practice.