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A Numerical Approach to the Rosenau-KdV equation using Galerkin Cubic Finite Element Method

Y. Ucar, B. Karaagac, S. Kutluay

Abstract


In this paper, a Galerkin finite element method has been used to solve numerically the Rosenau-KdV equation using cubic B-spline functions. The system of ordinary differential equations obtained in terms of element parameters by the application of the method has been solved by using the fourth order Runge-Kutta method. The error norms L_{2} and L_{infinity} together with invariants I_1 and I_2 have been calculated to show the accuracy and efficiency of the method.

The computed results have been compared with exact values and also other numerical results available in the literature.

Keywords


Galerkin finite element method, Rosenau-KdV equation, Runge-Kutta method, cubic B-spline, solitary wave.

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