A uniformly almost second order convergent numerical method for singularly perturbed delay differential equations

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.