Interior Layers in a Reaction-Diffusion Equation with a Discontinuous Diffusion Coefficient

Abstract

In this paper a problem arising in the modelling of semiconductor devices motivates the study of singularly perturbed differential equations of reaction-diffusion type with discontinuous data. The solutions of such problems typically contain interior layers where the gradient of the solution changes rapidly. Parameter-uniform methods based on piecewise-uniform Shishkin meshes are constructed and analysed for such problems. Numerical results are presented to support the theoretical results and to illustrate the benefits of using a piecewise-uniform Shishkin mesh over the use of uniform meshes in the simulation of a simple semiconductor device.