Erdogan, FevziSakar, Mehmet GiyasSaldir, Onur2025-05-102025-05-1020202444-865610.2478/AMNS.2020.1.000402-s2.0-85089140274https://doi.org/10.2478/AMNS.2020.1.00040https://hdl.handle.net/20.500.14720/13750Saldir, Onur/0000-0002-5292-9458The purpose of this paper is to present a uniform finite difference method for numerical solution of a initial value problem for semilinear second order singularly perturbed delay differential equation. A numerical method is constructed for this problem which involves appropriate piecewise-uniform Shishkin mesh on each time subinterval. The method is shown to uniformly convergent with respect to the perturbation parameter. A numerical experiment illustrate in practice the result of convergence proved theoretically.eninfo:eu-repo/semantics/openAccessDelay Differential EquationSingular PerturbationFinite Difference SchemePiecewise-Uniform MeshError EstimatesArticle51N/AQ3425436WOS:000664154800039