A second-order finite difference scheme for a class of singularly perturbed delay differential equations

Abstract

In this paper a class of delay differential equations with a perturbation parameter ϵ is examined. A hybrid finite difference scheme on an appropriate piecewise uniform mesh of Shishkin-type is derived. We show that the scheme is almost second-order convergent, in the discrete maximum norm, independent of singular perturbation parameter. Numerical experiments support these theoretical results.