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

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dc.contributor.authorEshkuvatov, ZKen_US
dc.contributor.authorZulkarnain, FSen_US
dc.contributor.authorLong, NMANen_US
dc.contributor.authorMuminov, Zen_US
dc.date.accessioned2024-05-29T02:58:24Z
dc.date.available2024-05-29T02:58:24Z
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.
dc.identifier.doi10.1186/s40064-016-3070-z
dc.identifier.issn2193-1801
dc.identifier.scopusWOS:000391797200008
dc.identifier.urihttps://oarep.usim.edu.my/handle/123456789/11690
dc.identifier.volume5
dc.languageEnglish
dc.language.isoen_US
dc.publisherSpringer International Publishing Agen_US
dc.relation.ispartofSpringerplus
dc.sourceWeb Of Science (ISI)
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 kind
dc.typeArticleen_US
dspace.entity.typePublication

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