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

• Published in: Bulletin of the Belgian Mathematical Society, Simon Stevin Vol. 19; no. 2; pp. 215 - 227
• Main Authors: Geyikli, Turabi, Gazi Karakoç, S. Battal
• Format: Journal Article
• Language: English
• Published: Belgian Mathematical Society 01.04.2012; The Belgian Mathematical Society
• Subjects: 65D07; 65N30; 76B25; Modified equal width wave (MEW) equation; Numerical analysis; Petrov-Galerkin method; Solitary waves; Spline theory; Splines; Wave equation; Turkey
• ISSN: 1370-1444; 2034-1970
• DOI: 10.36045/bbms/1337864268

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.sub.2], [L.sub.∞] 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. Key words and phrases: Petrov-Galerkin method, Modified equal width wave (MEW) equation, Splines, Solitary waves.