Petrov-Galerkin method with cubic B-splines for solving the MEW equation - Geyikli, Turabi; Gazi Karakoç, S. Battal (Bulletin of the Belgian Mathematical Society, Simon Stevin, 2012)
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.