Advances in Difference Equations
Volume 2009 (2009), Article ID 781579, 9 pages
doi:10.1155/2009/781579

An exponentially fitted method for singularly perturbed delay differential equations

Abstract

This paper deals with singularly perturbed initial value problem for linear first-order delay differential equation. An exponentially fitted difference scheme is constructed in an equidistant mesh, which gives first-order uniform convergence in the discrete maximum norm. The difference scheme is shown to be uniformly convergent to the continuous solution with respect to the perturbation parameter. A numerical example is solved using the presented method and compared the computed result with exact solution of the problem.