A NUMERICAL SOLUTION OF THE MODIFIED REGULARIZED LONG WAVE (MRLW) EQUATION USING QUARTIC B-SPLINES

A NUMERICAL SOLUTION OF THE MODIFIED REGULARIZED LONG WAVE (MRLW) EQUATION USING QUARTIC B-SPLINES

S. Battal Gazi Karakoc    Turabi Geyikli    Ali Bashan    

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Abstract

In this paper, a numerical solution of the modified regularized long wave (MRLW) equation is obtained by subdomain finite element method using quartic B-spline functions. Solitary wave motion, interaction of two and three solitary waves and the development of the Maxwellian initial condition into solitary waves are studied using the proposed method. Accuracy and efficiency of the proposed method are tested by calculating the numerical conserved laws and error norms L2 and L∞ . The obtained results show that the method is an effective numerical scheme to solve the MRLWequation. In addition, a linear stability analysis of the scheme is found to be unconditionally stable.

Keywords

MRLW equation, Finite element method, Subdomain, Quartic B-Splines, Solitary waves.