Exponential B-spline collocation solutions to the Gardner equation


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ERSOY HEPSON Ö., KORKMAZ A., Dag İ.

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, vol.97, no.4, pp.837-850, 2020 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Review
  • Volume: 97 Issue: 4
  • Publication Date: 2020
  • Doi Number: 10.1080/00207160.2019.1594791
  • Journal Name: INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded, Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, Computer & Applied Sciences, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.837-850
  • Keywords: Stability, numerical analysis, PDE, splines, solitary waves, WAVE SOLUTIONS, SOLITONS, SYSTEM

Abstract

Exponential B-splines are used to set up a collocation method for solving the Gardner equation. The space reduction of the Gardner equation is carried out to be able to obtain an exponential B-spline approximation for the collocation method. Thus, a coupled system is integrated using the Crank-Nicolson implicit method in time together with the first-order linearization method and then the collocation method is applied to have a linear algebraic system. This system is shown to be stable by using the Von Neumann analysis. The discrete maximum errors are found fairly small and relative changes of the conservation laws remain constant during simulations for the text problems.