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.