A 3-Scale Haar Wavelet Collocation Method for Numerical Solution of the Nonlinear Gardner Equation

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dc.contributor.authorBulut, Fatih
dc.contributor.authorOruc, Omer
dc.contributor.authorEsen, Alaattin
dc.date.accessioned2026-04-04T13:37:35Z
dc.date.available2026-04-04T13:37:35Z
dc.date.issued2025
dc.departmentİnönü Üniversitesi
dc.description.abstractIn this paper, a 3-scale Haar wavelet collocation method was applied to the nonlinear Gardner equation which can be used to describe the large-amplitude inner waves in the ocean. We start the solution process with the time discretization of the Gardner equation, with the help of finite difference method. Then, we have used 3-scale Haar wavelets for the space discretization. These steps gave us a system of algebraic equations, by solving these equations we were able to get wavelet coefficients and used them to construct the numerical solution of the Gardner equation. We applied the proposed method to five different problems to test the accuracy and compared the obtained results with other studies in the literature. The results and comparisons are given in tables and solutions are depicted graphically. The results show that the method proposed in this manuscript is highly accurate even with a low number of collocation points.
dc.description.sponsorshipScientific and Technological Research Council of Turkiye (TUBITAK)
dc.description.sponsorshipOpen access funding provided by the Scientific and Technological Research Council of Turkiye (TUBITAK).
dc.identifier.doi10.1007/s00009-025-02808-3
dc.identifier.issn1660-5446
dc.identifier.issn1660-5454
dc.identifier.issue2
dc.identifier.orcid0000-0002-6655-3543
dc.identifier.scopus2-s2.0-85219728459
dc.identifier.scopusqualityQ2
dc.identifier.urihttps://doi.org/10.1007/s00009-025-02808-3
dc.identifier.urihttps://hdl.handle.net/11616/109921
dc.identifier.volume22
dc.identifier.wosWOS:001424562600001
dc.identifier.wosqualityQ1
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherSpringer Basel Ag
dc.relation.ispartofMediterranean Journal of Mathematics
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_WOS_20250329
dc.subjectGardner equation
dc.subject3-scale Haar wavelet
dc.subjectnumerical solution
dc.subjectnonlinear equation
dc.titleA 3-Scale Haar Wavelet Collocation Method for Numerical Solution of the Nonlinear Gardner Equation
dc.typeArticle

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