A singularly perturbed reaction-diffusion problem with incompatible boundary-initial data

Abstract

A singularly perturbed reaction-diffusion parabolic problem with an incompatibility between the initial and boundary conditions is examined. A finite difference scheme is considered which utilizes a special finite difference operator and a piecewise uniform Shishkin mesh. Numerical results are presented for both nodal and global pointwise convergence, using bilinear interpolation and, also, an interpolation method based on the error function. These results show that the method is not globally convergent when bilinear interpolation is used but they indicate that, for the test problem considered, it is globally convergent using the second type of interpolation. © 2013 Springer-Verlag.