Cakir, MusaGunes, Baransel2025-05-102025-05-1020222227-739010.3390/math101935602-s2.0-85139743512https://doi.org/10.3390/math10193560https://hdl.handle.net/20.500.14720/10232Cakir, Musa/0000-0002-1979-570XThis paper presents a epsilon-uniform and reliable numerical scheme to solve second-order singularly perturbed Volterra-Fredholm integro-differential equations. Some properties of the analytical solution are given, and the finite difference scheme is established on a non-uniform mesh by using interpolating quadrature rules and the linear basis functions. An error analysis is successfully carried out on the Boglaev-Bakhvalov-type mesh. Some numerical experiments are included to authenticate the theoretical findings. In this regard, the main advantage of the suggested method is to yield stable results on layer-adapted meshes.eninfo:eu-repo/semantics/openAccessError AnalysisFinite Difference MethodFredholm Integro-Differential EquationSingular PerturbationVolterra Integro-Differential EquationUniform ConvergenceArticle1019Q1Q2WOS:000867122500001