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

Turabi Geyikli and S. Battal Gazi Karakoç
Source: Bull. Belg. Math. Soc. Simon Stevin Volume 19, Number 2 (2012), 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 $L_{2}$ , $L_{\infty }$ 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.

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Primary Subjects: 65N30, 65D07, 76B25
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