About fitted finite-difference operators and fitted meshes for solving singularly perturbed linear problems in one dimension

Abstract

Classical finite-difference operators on uniform meshes are not appropriate for solving singularly perturbed differential equations due to the effect of the boundary layers.If we want uniformly convergent difference schemes (with respect to some discrete norm), we need to adequate the numerical operator or the mesh, or both, the operator and the mesh. We summarize some recent results about uniform convergent methods for a general linear two point boundary value problem and present two algorithms related with the numerical method, which give indication about the transition points of the solution in the given domain. They are transition point indicators