Ekinci, Y.Cimen, E.Cakir, M.2025-09-032025-09-0320250965-54251555-666210.1134/S09655425257005872-s2.0-105012723423https://doi.org/10.1134/S0965542525700587https://hdl.handle.net/20.500.14720/28296In this paper, we deal with a singularly perturbed neutral-type delay differential problem. To solve this problem numerically, we construct a novel difference scheme on a layer-adapted mesh with the finite difference method by using interpolated quadrature rules with remainder terms in integral form. We prove that this scheme is first-order uniformly convergent with respect to the small perturbation parameter in discrete maximum norm. We also present numerical experiments which confirm the theoretical findings.eninfo:eu-repo/semantics/closedAccessDelay Differential EquationInitial Value ProblemFinite Difference MethodError EstimateUniform ConvergenceArticle656Q3Q313281343WOS:001551465700008