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A new class of orthogonal polynomials for solving logarithmic singular integral equations

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dc.contributor.authorAlhawamda H.en_US
dc.contributor.authorTaib B.M.en_US
dc.contributor.authorEshkuvatov Z.K.en_US
dc.contributor.authorIbrahim R.I.en_US
dc.date.accessioned2024-05-29T02:04:34Z
dc.date.available2024-05-29T02:04:34Z
dc.date.issued2020
dc.descriptionAin Shams Engineering Journal 11 (2020) 489–494en_US
dc.description.abstractIn this note, we propose a new class of orthogonal polynomials (named Bachok–Hasham polynomials H1nk(x)), which is an extension of the Chebyshev polynomials. Eigenfunctions and corresponding eigenvalues are found for the homogeneous second kind of Logarithmic Singular Integral Equations (LogSIEs). For non-homogeneous LogSIEs truncated series of the first kind Bachok–Hasham polynomials are used to find approximate solution. It is found that first kind of Bachok–Hasham polynomials (H1nk(x)) are orthogonal with weight [Formula presented], where k is positive odd integer. Properties of first kind of Bachok–Hasham polynomials are also proved. Finally, two examples are presented to show the validity and accuracy of the proposed method. © 2019 THE AUTHORSen_US
dc.identifier.doihttps://doi.org/10.1016/j.asej.2017.10.010
dc.identifier.epage494
dc.identifier.issn20904479
dc.identifier.issue2
dc.identifier.scopus2-s2.0-85075860777
dc.identifier.spage489
dc.identifier.urihttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85075860777&doi=10.1016%2fj.asej.2017.10.010&partnerID=40&md5=2ebe28bb81006c5682236373109dc697
dc.identifier.urihttps://www.sciencedirect.com/science/article/pii/S2090447919301340
dc.identifier.urihttps://oarep.usim.edu.my/handle/123456789/10299
dc.identifier.volume11
dc.languageEnglish
dc.language.isoen_USen_US
dc.publisherAin Shams Universityen_US
dc.relation.ispartofAin Shams Engineering Journalen_US
dc.sourceScopus
dc.subjectChebyshev polynomialsen_US
dc.subjectNew orthogonal basis functionsen_US
dc.subjectSingular integralen_US
dc.titleA new class of orthogonal polynomials for solving logarithmic singular integral equationsen_US
dc.typeArticleen_US
dspace.entity.typePublication

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