Computing

, Volume 73, Issue 2, pp 121–133

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

Article

DOI: 10.1007/s00607-004-0065-3

Cite this article as:
Linß, T. & Madden, N. Computing (2004) 73: 121. doi:10.1007/s00607-004-0065-3

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.

Keywords

Reaction diffusionsingular perturbationsolution decompositionShishkin mesh

Copyright information

© Springer-Verlag Wien 2004

Authors and Affiliations

  1. 1.Institut für Numerische MathematikTechnische Universität DresdenDresdenGermany
  2. 2.Department of MathematicsNational University of IrelandGalwayIreland