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Modified homotopy perturbation method for solving hypersingular integral equations of the first kind

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dc.citedby3
dc.contributor.affiliationsFaculty of Science and Technology
dc.contributor.affiliationsUniversiti Sains Islam Malaysia (USIM)
dc.contributor.affiliationsUniversiti Putra Malaysia (UPM)
dc.contributor.affiliationsSamarkand State University
dc.contributor.authorEshkuvatov Z.K.en_US
dc.contributor.authorZulkarnain F.S.en_US
dc.contributor.authorNik Long N.M.A.en_US
dc.contributor.authorMuminov Z.en_US
dc.date.accessioned2024-05-28T08:34:18Z
dc.date.available2024-05-28T08:34:18Z
dc.date.issued2016
dc.description.abstractModified homotopy perturbation method (HPM) was used to solve the hypersingular integral equations (HSIEs) of the first kind on the interval [?1,1] with the assumption that the kernel of the hypersingular integral is constant on the diagonal of the domain. Existence of inverse of hypersingular integral operator leads to the convergence of HPM in certain cases. Modified HPM and its norm convergence are obtained in Hilbert space. Comparisons between modified HPM, standard HPM, Bernstein polynomials approach Mandal and Bhattacharya (Appl Math Comput 190:1707?1716, 2007), Chebyshev expansion method Mahiub et al. (Int J Pure Appl Math 69(3):265�274, 2011) and reproducing kernel Chen and Zhou (Appl Math Lett 24:636�641, 2011) are made by solving five examples. Theoretical and practical examples revealed that the modified HPM dominates the standard HPM and others. Finally, it is found that the modified HPM is exact, if the solution of the problem is a product of weights and polynomial functions. For rational solution the absolute error decreases very fast by increasing the number of collocation points. � 2016, The Author(s).
dc.description.natureFinalen_US
dc.identifier.ArtNo1473
dc.identifier.doi10.1186/s40064-016-3070-z
dc.identifier.issn21931801
dc.identifier.issue1
dc.identifier.scopus2-s2.0-84984903211
dc.identifier.urihttps://www.scopus.com/inward/record.uri?eid=2-s2.0-84984903211&doi=10.1186%2fs40064-016-3070-z&partnerID=40&md5=507dce536792b42b7d9ebce817483393
dc.identifier.urihttps://oarep.usim.edu.my/handle/123456789/9086
dc.identifier.volume5
dc.languageEnglish
dc.language.isoen_USen_US
dc.publisherSpringerOpenen_US
dc.relation.ispartofSpringerPlus
dc.sourceScopus
dc.subjectHomotopy perturbation methoden_US
dc.subjectHypersingular integral equationen_US
dc.subjectIntegral equationen_US
dc.titleModified homotopy perturbation method for solving hypersingular integral equations of the first kinden_US
dc.title.alternativeSpringerPlusen_US
dc.typeArticleen_US
dspace.entity.typePublication

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