A numerical method is proposed for linear second-order singularly perturbed delay differential equations of the form
subject to Dirichlet boundary conditions. Here, is the perturbation parameter and is the small shift parameter. The authors are mainly focused on the case .
In order to solve this problem classical finite difference schemes are used with the mesh parameter , where , is a positive integer and is the mantissa of . The truncation error contains the higher-order derivatives of the solution of the continuous problem which involve negative powers of the small (perturbation and delay) parameters. Therefore, the convergence result provided here may not be independent of the parameters, that is, they are not uniformly-convergent. Some numerical examples are presented.