An Almost Sixth-Order Finite-Difference Method for Semilinear Singular Perturbation Problems

Abstract

The discretization meshes of the Shishkin type are more suitable for high- orderfinite-difference schemes than Bakhvalov-type meshes. This point is illustrated by the construction of a hybrid scheme for a class of semilinear singularly perturbed reaction-diffusion problems. A sixth-order five-point equidistant scheme is used at most of the mesh points inside the boundary layers, whereas lower-order three-point schemes are used elsewhere. It is proved under certain conditions that this combined scheme is almost sixth-order accurate and that its error does not increase when the perturbation parameter tends to zero. © 2004, Institute of Mathematics, NAS of Belarus. All rights reserved.