Numerical Solution of the Rosenau-KdV-RLW equation via combination of a polynomial scaling function collocation and finite difference method

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dc.contributor.authorOruc, Omer
dc.contributor.authorEsen, Alaattin
dc.contributor.authorBulut, Fatih
dc.date.accessioned2026-04-04T13:37:37Z
dc.date.available2026-04-04T13:37:37Z
dc.date.issued2025
dc.departmentİnönü Üniversitesi
dc.description.abstractIn this paper, we established a polynomial scaling method to investigate the numerical solution of Rosenau-Korteweg De Vries-regularized long wave (Rosenau-KdV-RLW) equation. We start with discretization of the time variable of the equation using a finite difference approach equipped with a linearization. After the time discretization, we have used polynomial scaling functions for the discretization of the spatial variable. These two discretizations give us the desired discrete system of equations to obtain numerical solutions. We further derive an error estimate for the proposed method. We have applied the proposed method to Rosenau-KdV, Rosenau-RLW, and Rosenau-KdV-RLW equations and used error norms to examine the accuracy and reliability of the presented method. Also, to enhance accuracy of the results, we utilize Richardson extrapolation. The comparisons with the analytical solution and earlier studies that use different methods indicate that the proposed method is accurate and reliable.
dc.description.sponsorshipNo fund is received for this work. The authors would like to thank to anonymous reviewers for their precious time and suggestions toward improving the paper.
dc.identifier.doi10.1002/mma.10531
dc.identifier.endpage4034
dc.identifier.issn0170-4214
dc.identifier.issn1099-1476
dc.identifier.issue3
dc.identifier.orcid0000-0002-7927-5941
dc.identifier.orcid0000-0002-6655-3543
dc.identifier.orcid0000-0001-6603-2468
dc.identifier.scopus2-s2.0-85206812589
dc.identifier.scopusqualityQ1
dc.identifier.startpage4015
dc.identifier.urihttps://doi.org/10.1002/mma.10531
dc.identifier.urihttps://hdl.handle.net/11616/109949
dc.identifier.volume48
dc.identifier.wosWOS:001334376900001
dc.identifier.wosqualityQ1
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherWiley
dc.relation.ispartofMathematical Methods in the Applied Sciences
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_WOS_20250329
dc.subjectcollocation
dc.subjectnumerical solution
dc.subjectpolynomial scaling method
dc.subjectRosenau KdV-RLW
dc.titleNumerical Solution of the Rosenau-KdV-RLW equation via combination of a polynomial scaling function collocation and finite difference method
dc.typeArticle

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