Accurate Solution of a System of Coupled Singularly Perturbed Reaction-diffusion Equations

Authors:
T. Linß;N. Madden
Affiliations:
Technische Universität Dresden, Institut für Numerische Mathematik, 01062, Dresden, Germany;National University of Ireland, Department of Mathematics, 01062, Galway, Ireland
Venue:
Computing
Year:
2004

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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 [5]. We present the results of numerical experiments to confirm our theoretical results.