A quartic trigonometric tension B-spline finite element method for solving Gardner equation

ERSOY HEPSON Ö.

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, vol.38, no.4, pp.1055-1067, 2022 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 38 Issue: 4
  • Publication Date: 2022
  • Doi Number: 10.1002/num.22787
  • Journal Name: NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, Compendex, MathSciNet, zbMATH, DIALNET, Civil Engineering Abstracts
  • Page Numbers: pp.1055-1067
  • Keywords: convergence analysis, Gardner equation, quartic trigonometric tension B-spline, DYNAMICS
  • Eskisehir Osmangazi University Affiliated: Yes

Abstract

The collocation method is established for getting solution of the Gardner equation (GE). The GE is fully integrated by way of the Crank-Nicolson method for time variable and collocation method for spatial variable. Trial function of the collocation method is set up using combination of quartic trigonometric tension (QTT) B-splines. Convergence analysis of suggested method is investigated. Performance of the QTT B-splines is searched by studying three test problems: propagation of bell shape solitary wave, interaction of two positive bell shape solitary wave and wave generation.