Petrov-Galerkin method with cubic B-splines for solving the MEW equation


Geyikli T., KARAKOÇ S. B. G.

BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN, vol.19, no.2, pp.215-227, 2012 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 19 Issue: 2
  • Publication Date: 2012
  • Doi Number: 10.36045/bbms/1337864268
  • Journal Name: BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.215-227

Abstract

In the present paper, we introduce a numerical solution algorithm based on a Petrov-Galerkin method in which the element shape functions are cubic B-splines and the weight functions quadratic B-splines. The motion of a single solitary wave and interaction of two solitary waves are studied. Accuracy and efficiency of the proposed method are discussed by computing the numerical conserved laws and L-2, L-infinity error norms. The obtained results show that the present method is a remarkably successful numerical technique for solving the modified equal width wave(MEW) equation. A linear stability analysis of the scheme shows that it is unconditionally stable.