A uniformly convergent method for a singularly perturbed semilinear reaction-diffusion problem with discontinuous data

This paper deals with a uniform (in a perturbation parameter) convergent difference scheme for solving a nonlinear singularly perturbed two-point boundary value problem with discontinuous data of a reaction-diffusion type. An error analysis is based on locally exact schemes. Uniform convergence of the proposed difference scheme on piecewise uniform and log-meshes is proven. A monotone iterative method, which is based on the method of upper and lower solutions, is applied to computing the nonlinear difference scheme. Numerical experiments are presented. (c) 2006 Elsevier Inc. All rights reserved.