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.