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oai:ebyu-rdlopen.rawdatalibrary.net:ebyu/132812026-10-18T20:41:31Zopenairedrivercom_ebyu_10000col_ebyu_10001

A second order numerical method for singularly perturbed problem with non-local boundary conditionCakir, MusaAmiraliyev, Gabil M.Exponentially fitted difference schemeNonlocal conditionSecond-order accuracySingular perturbationUniformly convergenceBoundary value problemsDifference schemesIntegral identitiesNon-local boundary conditionsQuadrature rulesSingular perturbationsSingularly perturbedSingularly perturbed problemUniformly convergentNumerical methodsThe aim of this paper is to present a monotone numerical method on uniform mesh for solving singularly perturbed three-point reaction–diffusion boundary value problems. Firstly, properties of the exact solution are analyzed. Difference schemes are established by the method of the integral identities with the appropriate quadrature rules with remainder terms in integral form. It is then proved that the method is second-order uniformly convergent with respect to singular perturbation parameter, in discrete maximum norm. Finally, one numerical example is presented to demonstrate the efficiency of the proposed method. © 2021, Korean Society for Informatics and Computational Applied Mathematics.Springer Science and Business Media Deutschland GmbH2021Articlehttps://rdlopen.rawdatalibrary.net/r/ebyu/13281https://doi.org/10.1007/s12190-021-01506-z1598-5865enJournal of Applied Mathematics and Computinginfo:eu-repo/semantics/openAccessinfo:eu-repo/semantics/articlehttps://ebyu-rdlopen.rawdatalibrary.net/tr/items/ebyu/13281