A class of finite difference schemes for singularly perturbed delay differential equations of second order

Abstract

In this paper, we proposed a new class of finite difference schemes for solving singularly perturbed delaydifferential equation of second order. The proposed schemes are oscillation-free and more accurate than conventionalschemes on a uniform mesh. These schemes are easily adaptable on special meshes like Shishkin mesh or Bakhvalovmesh and are uniformly convergent with respect to the perturbation parameter. The error analysis has been carried outand numerical examples are presented to show the accuracy and efficiency of the proposed schemes.