Numerical solutions of Boussinesq equation using Galerkin finite element method

UÇAR Y., ESEN A., Karaagac B.

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, vol.37, no.2, pp.1612-1630, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 37 Issue: 2
  • Publication Date: 2021
  • Doi Number: 10.1002/num.22600
  • 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.1612-1630
  • Keywords: bad Boussinesq equation, B-spline, finite element method, Galerkin method, good Boussinesq equation, interaction, Runge-Kutta method, solitary wave, SOLITON, WAVES
  • Inonu University Affiliated: Yes

Abstract

In this study, Galerkin finite element method has been applied to good Boussinesq (GBq) and bad Boussinesq (BBq) equations which are examples of Boussinesq type equations. To apply the method, cubic B-spline basis functions are taken as element and weight functions. The solutions of the numerical schemes have been obtained using the fourth order Runge-Kutta method. The error norms L-2 and L-infinity have been used to test how compatible they obtained numerical solutions with those of exact ones. As numerical examples, solitary wave motion and interaction of solitary waves have been investigated for both GBq and BBq equation. Also blow-up solutions related to the interaction of two solitary waves are considered for GBq equation.