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Absolutely stable difference scheme for a general class of singular perturbation problems

dc.contributor.authorEl-Zahar, Essam R.
dc.contributor.authorAlotaibi, A. M.
dc.contributor.authorEbaid, Abdelhalim
dc.contributor.authorBaleanu, Dumitru
dc.contributor.authorMachado, Jose Tenreiro
dc.contributor.authorHamed, Y. S.
dc.contributor.authorID56389tr_TR
dc.date.accessioned2020-12-25T11:13:34Z
dc.date.available2020-12-25T11:13:34Z
dc.date.issued2020
dc.departmentÇankaya Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümüen_US
dc.description.abstractThis paper presents an absolutely stable noniterative difference scheme for solving a general class of singular perturbation problems having left, right, internal, or twin boundary layers. The original two-point second-order singular perturbation problem is approximated by a first-order delay differential equation with a variable deviating argument. This delay differential equation is transformed into a three-term difference equation that can be solved using the Thomas algorithm. The uniqueness and stability analysis are discussed, showing that the method is absolutely stable. An optimal estimate for the deviating argument is obtained to take advantage of the second-order accuracy of the central finite difference method in addition to the absolute stability property. Several problems having left, right, interior, or twin boundary layers are considered to validate and illustrate the method. The numerical results confirm that the deviating argument can stabilize the unstable discretized differential equation and that the new approach is effective in solving the considered class of singular perturbation problems.en_US
dc.description.publishedMonth8
dc.identifier.citationEl-Zahar, Essam R...et al. (2020). "Absolutely stable difference scheme for a general class of singular perturbation problems", Advances in Difference Equations, vol. 2020, No. 1.en_US
dc.identifier.doi10.1186/s13662-020-02862-z
dc.identifier.issn1687-1847
dc.identifier.issue1en_US
dc.identifier.urihttp://hdl.handle.net/20.500.12416/4402
dc.identifier.volume2020en_US
dc.language.isoenen_US
dc.relation.ispartofAdvances in Difference Equationsen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectSingular Perturbation Problemsen_US
dc.subjectFinite Difference Schemesen_US
dc.subjectAbsolutely Stableen_US
dc.subjectBoundary and Interior Layersen_US
dc.titleAbsolutely stable difference scheme for a general class of singular perturbation problemstr_TR
dc.titleAbsolutely Stable Difference Scheme for a General Class of Singular Perturbation Problemsen_US
dc.typeArticleen_US
dspace.entity.typePublication

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