Cakir, MusaGunes, Baransel2025-05-102025-05-1020222651-477X10.15672/hujms.9500752-s2.0-85131246458https://doi.org/10.15672/hujms.950075https://hdl.handle.net/20.500.14720/8311Cakir, Musa/0000-0002-1979-570XIn this research, the finite difference method is used to solve the initial value problem of linear first order Volterra-Fredholm integro-differential equations with singularity. By using implicit difference rules and composite numerical quadrature rules, the difference scheme is established on a Shishkin mesh. The stability and convergence of the proposed scheme are analyzed and two examples are solved to display the advantages of the presented technique.eninfo:eu-repo/semantics/openAccessKeywordsDifference SchemeError EstimateFredholm Integro-Differential EquationSingular PerturbationShishkin MeshVolterra Integro-Differential EquationArticle513Q3Q37877991162771WOS:000807503800013