A second order accurate, positive scheme for singularly perturbed boundary value problems

摘要

We give a novel finite difference method for singularly perturbed boundary value problems in$$mathbb{R}^{text{1}}$$. The method is of positive type in 1−Dwith errors ofO(h2+ εh) in regions a few meshpoints away from possible layers, where ε is the small parameter in the differential equation. Global and local error estimates are proven for the method and numerical experiments are presented. Possible extension to 2−Das a monotone scheme is considered, but more questons are unsolved than solved i