Fitted-Modified Upwind Finite Difference Method for Solving Singularly Perturbed Differential Difference Equations

Abstract

A fitted modified upwind finite difference method is presented for solving singularly perturbed boundary value problems with delay δ and advance η parameters that are sufficiently small. The second order singularly perturbed differential difference equation is replaced by an asymptotically equivalent singularly perturbed boundary value problem. A fitting factor is introduced in a modified finite difference scheme and is obtained from the theory of singular perturbations. Thomas Algorithm is used to solve the system and its stability is investigated. The method is demonstrated by implementing several model examples by taking various values for the delay parameterδ , advance parameter η and the perturbation parameterε .