On a modified Bernstein operators approximation method for computational solution of Volterra integral equation

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dc.contributor.authorAnsari, Khursheed J.
dc.contributor.authorUsta, Fuat
dc.date.accessioned2025-10-11T20:48:03Z
dc.date.available2025-10-11T20:48:03Z
dc.date.issued2025
dc.departmentDüzce Üniversitesien_US
dc.description.abstractThe main feature of this paper is an application of the modified Bernstein operator in the approximate and numerical solution of integral equations. The stability of the algorithm is discussed in the context of errors resulting from the numerical approximation of Volterra integral equations. The mechanism of the proposed method is explained in detail, including its main features. Furthermore, a comparison with an alternative numerical technique is made, and the superiority of the proposed solution is shown. Numerical experiments are also performed to verify the validity of the proposed method and to assess its accuracy. Finally, several conclusions are drawn from the results of the numerical experiments. The proposed method provides a powerful and efficient tool for the approximate solution of Volterra integral equations, and its results are promising. The results obtained from this algorithm are useful in the numerical analysis of integral equations.en_US
dc.description.sponsorshipDeanship of Research and Graduate Studies at King Khalid University [RGP2/203/45]en_US
dc.description.sponsorshipThe first author (K.J.A) extends his appreciation to the Deanship of Research and Graduate Studies at King Khalid University for funding this work through Large Research Project under grant number RGP2/203/45.en_US
dc.identifier.doi10.1186/s13660-024-03225-y
dc.identifier.issn1029-242X
dc.identifier.issue1en_US
dc.identifier.scopus2-s2.0-85217542865en_US
dc.identifier.scopusqualityN/Aen_US
dc.identifier.urihttps://doi.org/10.1186/s13660-024-03225-y
dc.identifier.urihttps://hdl.handle.net/20.500.12684/21735
dc.identifier.volume2025en_US
dc.identifier.wosWOS:001400438300001en_US
dc.identifier.wosqualityQ1en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherSpringeren_US
dc.relation.ispartofJournal of Inequalitiesand Applicationsen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.snmzKA_WOS_20250911
dc.subjectModified Bernstein's approximation techniqueen_US
dc.subjectVolterra integral equation of the first and second kinden_US
dc.subjectNumerical schemeen_US
dc.subjectConvergence analysisen_US
dc.titleOn a modified Bernstein operators approximation method for computational solution of Volterra integral equationen_US
dc.typeArticleen_US

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