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An efficient numerical method for a singularly perturbed Fredholm integro-differential equation with integral boundary conditionDurmaz, Muhammet EnesAmirali, IlhameAmiraliyev, Gabil M.Finite difference schemeFredholm integro-differential equationIntegral boundary conditionShishkin meshSingular perturbationUniform convergenceBoundary conditionsConvergence of numerical methodsFinite difference methodIntegrodifferential equationsMesh generationEfficient numerical methodFredholmFredholm integro-differential equationsInitial-value problemIntegral boundary conditionsShishkin meshesSingular perturbationsSingularly perturbedInitial value problemsIn this paper, a linear singularly perturbed Fredholm integro-differential initial value problem with integral condition is being considered. On a Shishkin-type mesh, a fitted finite difference approach is applied using a composite trapezoidal rule in both; in the integral part of equation and in the initial condition. The proposed technique acquires a uniform second-order convergence in respect to perturbation parameter. Further provided the numerical results to support the theoretical estimates. © 2022, The Author(s) under exclusive licence to Korean Society for Informatics and Computational Applied Mathematics.Institute for Ionics2023Articlehttps://rdlopen.rawdatalibrary.net/r/ebyu/12272https://doi.org/10.1007/s12190-022-01757-41598-5865enJournal of Applied Mathematics and Computinginfo:eu-repo/semantics/openAccessinfo:eu-repo/semantics/articlehttps://ebyu-rdlopen.rawdatalibrary.net/tr/items/ebyu/12272