Gunes, BaranselCakir, Musa2025-05-102025-05-1020230965-54251555-666210.1134/S09655425231201142-s2.0-85183619746https://doi.org/10.1134/S0965542523120114https://hdl.handle.net/20.500.14720/15474This paper purposes to present a new discrete scheme for the singularly perturbed semilinear Volterra-Fredholm integro-differential equation including two integral boundary conditions. Initially, some analytical properties of the solution are given. Then, using the composite numerical integration formulas and implicit difference rules, the finite difference scheme is established on a uniform mesh. Error approximations for the approximate solution and stability bounds are investigated in the discrete maximum norm. Finally, a numerical example is solved to show epsilon-uniform convergence of the suggested difference scheme.eninfo:eu-repo/semantics/closedAccessDiscrete SchemeError BoundsIntegral Boundary ConditionIntegro-Differential EquationSingular PerturbationArticle6312Q4Q325132527WOS:001152574300021