Uniform Numerical Method for Singularly Perturbed Delay Differential Equations

Abstract

This paper deals with the singularly perturbed initial value problem for a linear first-order delay differential equation. A numerical method is constructed for this problem which involves an appropriate piecewise-uniform mesh on each time subinterval. The difference scheme is shown to converge to the continuous solution uniformly with respect to the perturbation parameter. Numerical results are presented. (c) 2007 Elsevier Ltd. All rights reserved.