AFitted Numerov Method for Singular Perturbation Problems Exhibiting Twin Layers

Abstract

In this paper a fitted fourth-order finite difference scheme is presented for solving singularly perturbed two-point boundary value problems with the boundary layer at both end (left and right) points. We have introduced a fitting factor in Numerov fourth-order tridiagonal finite difference scheme and is obtained from the theory of singular perturbations. Thomas algorithm is used to solve the tridiagonal system. Several numerical examples are solved and compared with exact solution. It is observed that the present method approximates the exact solution very well.