An ϵ-uniform fitted operator method for solving boundary-value problems for singularly perturbed delay differential equations: Layer behavior

Abstract

In this paper, an ϵ-uniform fitted operator method which solves boundary-value problems for singularly perturbed differential-difference equations containing small delay with boundary layer behavior is presented. Both the cases, i.e., when boundary layer is on the left side and when boundary layer is on the right side are discussed here. It is shown that the scheme is ϵ-uniform by establishing the error estimate. The effect of small delay on the boundary layer solution is shown by considering several numerical experiments. Numerical results in terms of maximum errors are tabulated and plots giving computed and exact solution demonstrate the efficiency of the method.