Singularly perturbed reaction–diffusion problems with discontinuities in the initial and/or the boundary data

Abstract

Numerical approximations to the solutions of three different problem classes of singularly perturbed parabolic reaction–diffusion problems, each with a discontinuity in the boundary-initial data, are generated. For each problem class, an analytical function associated with the discontinuity in the data, is identified. Parameter-uniform numerical approximations to the difference between the analytical function and the solution of the singularly perturbed problem are generated using piecewise-uniform Shishkin meshes. Numerical results are given to illustrate all the theoretical error bounds established in the paper.