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A novel second-order fitted computational method for a singularly perturbed Volterra integro-differential equation

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Özet

In this paper, we deal with the second-order accurate homogeneous (non-hybrid) type difference scheme for solving a singularly perturbed first-order Volterra integro-differential equation. It is shown that the method displays uniform convergence of O(N−2 ln N) on a special non-uniform mesh, where N is the mesh parameter. Numerical results are included to verify the theoretical estimates. © 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group.

Anahtar Kelimeler

finite differencesingular perturbationuniform convergenceVolterra integro-differential equationFinite difference methodMesh generationDifference schemesNon-uniform meshNumerical resultsSecond ordersSingular perturbationsSingularly perturbedVolterra integro-differential equationsIntegrodifferential equations
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AlanDeğerDil
dc.contributor.authorYapman, Ömer
dc.contributor.authorAmiraliyev, Gabil M.
dc.date.accessioned2026-10-18T20:28:48.374084404Z
dc.date.available2026-10-18T20:28:48.374084404Z
dc.date.issued2020
dc.description.abstractIn this paper, we deal with the second-order accurate homogeneous (non-hybrid) type difference scheme for solving a singularly perturbed first-order Volterra integro-differential equation. It is shown that the method displays uniform convergence of O(N−2 ln N) on a special non-uniform mesh, where N is the mesh parameter. Numerical results are included to verify the theoretical estimates. © 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group.
dc.identifier.doi10.1080/00207160.2019.1614565
dc.identifier.eissn1029-0265
dc.identifier.endpage1302
dc.identifier.issn0020-7160
dc.identifier.issue6
dc.identifier.scopus2-s2.0-85065838577
dc.identifier.startpage1293
dc.identifier.urihttps://rdlopen.rawdatalibrary.net/r/ebyu/14009
dc.identifier.volume97
dc.identifier.wosWOS:000469721900001
dc.language.isoen
dc.publisherTaylor and Francis Ltd.
dc.relation.ispartofInternational Journal of Computer Mathematics
dc.rightsinfo:eu-repo/semantics/openAccess
dc.subjectfinite difference
dc.subjectsingular perturbation
dc.subjectuniform convergence
dc.subjectVolterra integro-differential equation
dc.subjectFinite difference method
dc.subjectMesh generation
dc.subjectDifference schemes
dc.subjectNon-uniform mesh
dc.subjectNumerical results
dc.subjectSecond orders
dc.subjectSingular perturbations
dc.subjectSingularly perturbed
dc.subjectVolterra integro-differential equations
dc.subjectIntegrodifferential equations
dc.titleA novel second-order fitted computational method for a singularly perturbed Volterra integro-differential equation
dc.typeArticle
dspace.entity.typePublication
rdl.citation.scopus38
rdl.citation.wos42
rdl.source.indexSCOPUS
rdl.source.indexWOS
rdl.wos.indexScience Citation Index Expanded (SCI-EXPANDED)