A second order uniformly convergent numerical scheme for parameterized singularly perturbed delay differential problems

Abstract

In this work, we propose a hybrid difference scheme for solving parameterized singularly perturbed delay differential problems. A unified error analysis framework for the proposed hybrid scheme is given that allows to conclude uniform convergence of $\mathcal {O}(N^{-2}\ln ^{2} N)$ on Shishkin meshes and $\mathcal {O}(N^{-2})$ on Bakhvalov meshes, where N is the number of mesh intervals in the domain. Numerical results are included to confirm the theoretical estimates.