A trigonometric quintic B-spline collocation technique for the fifth-order KdV-Burgers-Fisher equation

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dc.contributor.authorKaraagac, Berat
dc.contributor.authorEsen, Alaattin
dc.contributor.authorUcar, Yusuf
dc.contributor.authorYagmurlu, Nuri Murat
dc.date.accessioned2026-04-04T13:37:35Z
dc.date.available2026-04-04T13:37:35Z
dc.date.issued2025
dc.departmentİnönü Üniversitesi
dc.description.abstractThe paper investigates numerical solutions to the KdV-Burgers-Fisher (KBF) equation, which models a dispersion-dissipation-reaction phenomenon. The stated equation is a mathematical structure for describing physical, chemical, or biological systems in which the dynamics of the system are shaped by the interaction of dispersion, dissipation, and reaction processes. To solve the KBF equation, a collocation method based on the finite element approach is utilized. In order to construct the approximate solutions satisfying the governing equation at collocation points, the finite element shape functions have been selected as quintic trigonometric B-spline basis functions. The application of the collocation method to the equation yields an algebraic equation system that has a well-known penta-diagonal coefficient matrix. The resulting system allows us to calculate the error norms L2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_{2}$$\end{document} and L infinity\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_{\infty }$$\end{document} and simulate space-time graphics of numerical solutions. As numerical examples of the KdV-Burgers-Fisher (KBF) equation, two test problems are presented to show the performance of the collocation method, while the error norms and graphs including comparison with exact solutions are used to prove the correctness and applicability of the method. Moreover, existence and uniqueness of the solutions are discussed via fixed-point theory, stability analysis which is investigated via von-Neumann technique are presented in this paper as well.
dc.description.sponsorshipScientific and Technological Research Council of Turkiye (TUBIdot;TAK)
dc.description.sponsorshipOpen access funding provided by the Scientific and Technological Research Council of Turkiye (TUB & Idot;TAK).
dc.identifier.doi10.1007/s00366-025-02131-1
dc.identifier.endpage4171
dc.identifier.issn0177-0667
dc.identifier.issn1435-5663
dc.identifier.issue6
dc.identifier.orcid0000-0003-1593-0254
dc.identifier.scopus2-s2.0-105004434612
dc.identifier.scopusqualityQ1
dc.identifier.startpage4155
dc.identifier.urihttps://doi.org/10.1007/s00366-025-02131-1
dc.identifier.urihttps://hdl.handle.net/11616/109902
dc.identifier.volume41
dc.identifier.wosWOS:001483823400001
dc.identifier.wosqualityQ1
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherSpringer
dc.relation.ispartofEngineering With Computers
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_WOS_20250329
dc.subjectFifth order KdV-Burgers-Fisher equation
dc.subjectCollocation method
dc.subjectQuintic trigonometric B-spline basis
dc.subjectStability
dc.titleA trigonometric quintic B-spline collocation technique for the fifth-order KdV-Burgers-Fisher equation
dc.typeArticle

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