A reproducing kernel Hilbert space method for nonlinear partial differential equations: applications to physical equations

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dc.authoridAttia, Nourhane/0000-0002-9937-8665
dc.contributor.authorAttia, Nourhane
dc.contributor.authorAkgul, Ali
dc.date.accessioned2024-12-24T19:28:29Z
dc.date.available2024-12-24T19:28:29Z
dc.date.issued2022
dc.departmentSiirt Üniversitesi
dc.description.abstractThe partial differential equations (PDEs) describe several phenomena in wide fields of engineering and physics. The purpose of this paper is to employ the reproducing kernel Hilbert space method (RKHSM) in obtaining effective numerical solutions to nonlinear PDEs, which are arising in acoustic problems for a fluid flow. In this paper, the RKHSM is used to construct numerical solutions for PDEs which are found in physical problems such as sediment waves in plasma, sediment transport in rivers, shock waves, electric signals' transmission along a cable, acoustic problems for a fluid flow, vibrating membrane, and vibrating string. The RKHSM systematically produces analytic and approximate solutions in the form of series. The convergence analysis and error estimations are discussed to prove the applicability theoretically. Three applications are tested to show the performance and efficiency of the used method. Computational results indicated a good agreement between the exact and numerical solutions.
dc.identifier.doi10.1088/1402-4896/ac8958
dc.identifier.issn0031-8949
dc.identifier.issn1402-4896
dc.identifier.issue10
dc.identifier.scopus2-s2.0-85137688875
dc.identifier.scopusqualityQ1
dc.identifier.urihttps://doi.org/10.1088/1402-4896/ac8958
dc.identifier.urihttps://hdl.handle.net/20.500.12604/7081
dc.identifier.volume97
dc.identifier.wosWOS:000849437700001
dc.identifier.wosqualityQ2
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherIop Publishing Ltd
dc.relation.ispartofPhysica Scripta
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/closedAccess
dc.snmzKA_20241222
dc.subjectnumerical method for nonlinear problems
dc.subjectRKHS method
dc.subjectpartial differential equations
dc.subjectwave equations
dc.subjectconvergence analysis
dc.titleA reproducing kernel Hilbert space method for nonlinear partial differential equations: applications to physical equations
dc.typeArticle

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