A Uniformly Almost Second Order Convergent Numerical Method for Singularly Perturbed Delay Differential Equations

Abstract

The purpose of this paper is to present a uniform finite difference method for the numerical solution of a second order singularly perturbed delay differential equation. The problem is solved by using a hybrid difference scheme on a Shishkin-type mesh. The method is shown to be uniformly convergent with respect to the perturbation parameter. Numerical experiments illustrate in practice the result of convergence proved theoretically. (C) 2017 Elsevier B.V. All rights reserved.