Closed-form solutions of higher order parabolic equations in multiple dimensions: A reliable computational algorithm

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dc.authoridSaeed, Syed Tauseef/0009-0001-4221-052X
dc.authoridQayyum, Mubashir/0000-0002-6701-5640
dc.contributor.authorQayyum, Mubashir
dc.contributor.authorKhan, Amna
dc.contributor.authorSaeed, Syed Tauseef
dc.contributor.authorAkgul, Ali
dc.contributor.authorRiaz, Muhammad Bilal
dc.date.accessioned2024-12-24T19:25:18Z
dc.date.available2024-12-24T19:25:18Z
dc.date.issued2023
dc.departmentSiirt Üniversitesi
dc.description.abstractParabolic equations play an important role in chemical engineering, vibration theory, particle diffusion and heat conduction. Solutions of such equations are required to analyze and pre-dict changes in physical systems. Solutions of such equations require efficient and effective tech-niques to get reasonable accuracy in lesser time. For this purpose, current article proposes residual power series algorithm for higher order parabolic equations with variable coefficients in multiple dimensions. The proposed algorithm provides closed-form solutions without linearization, discretization or perturbation. For efficiency testing of the proposed methodology, initially it is implemented to homogeneous multidimensional parabolic models, and exact solutions are com-puted. In next stage of testing, proposed algorithm is enforced to three-dimensional non-homoge-neous fourth order parabolic equation, and closed form solutions are recovered. The obtained results indicate the validity and effectiveness of proposed methodology, hence proposed algorithm can be extended to more complex scenarios in engineering and sciences. (c) 2023 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).
dc.identifier.doi10.1016/j.aej.2023.03.031
dc.identifier.endpage489
dc.identifier.issn1110-0168
dc.identifier.issn2090-2670
dc.identifier.scopus2-s2.0-85151275565
dc.identifier.scopusqualityQ1
dc.identifier.startpage479
dc.identifier.urihttps://doi.org/10.1016/j.aej.2023.03.031
dc.identifier.urihttps://hdl.handle.net/20.500.12604/6332
dc.identifier.volume71
dc.identifier.wosWOS:000969063700001
dc.identifier.wosqualityQ1
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherElsevier
dc.relation.ispartofAlexandria Engineering Journal
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_20241222
dc.subjectPartial differential equations
dc.subjectResidual power series
dc.subjectParabolic equations
dc.subjectSeries solution
dc.titleClosed-form solutions of higher order parabolic equations in multiple dimensions: A reliable computational algorithm
dc.typeArticle

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