A parameter-uniform numerical method for a boundary value problem for a singularly perturbed delay differential equation

Abstract

In this paper, a boundary value problem for a second-order singularly perturbed delay differential equation is considered. The solution of this problem exhibits boundary layers at x = 0 and x = 2 and interior layers at x = 1. A numerical method composed of a classical finite difference scheme applied on a piecewise-uniform Shishkin mesh is suggested to solve the problem. The method is proved to be first-order convergent in the maximum norm uniformly in the perturbation parameter. Numerical illustrations support the theory.