The [formula omitted]-uniform convergence of a defect correction method on a Shishkin mesh

Abstract

A defect correction method based on finite difference schemes is considered for a singularly perturbed boundary value problem on a Shishkin mesh. The method combines the stability of the upwind difference scheme and the higher-order convergence of the central difference scheme. The almost second-order convergence of the scheme with respect to the discrete maximum norm, uniformly in the perturbation parameter ε, is proved. Numerical experiments support the theoretical results.