Accurate solution of a system of coupled singularly perturbed reaction-diffusion equations

T. Linß and N. Madden

Abstract

We study a system of coupled reaction-diffusion equations. The equations have diffusion parameters of different magnitudes associated with them. Near each boundary, their solution exhibit two overlapping layers. A central difference scheme on layer-adapted piecewise uniform meshes is used to solve the system numerically. We show that the scheme is almost second-order convergent, uniformly in both perturbation parameters, thus improving previous results [Madden & Stynes 2002]. We present the results of numerical experiments to confirm our theoretical results.

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