# A numerical study using finite element method for generalized Rosenau-Kawahara-RLW equation

Document Type : Research Paper

Authors

1 Department of Mathematics, Faculty of Science and Art, Nevsehir Haci Bektas Veli University, 50300 Nevsehir, Turkey

2 Department of Mathematics, University of Dhaka, 1000 Dhaka, Bangladesh

3 School of Mathematics, Shandong University, Shanda Nanlu 27, Jinan 250100, Shandong, P. R. China

Abstract

In this paper, we are going to obtain the soliton solution of the generalized Rosenau-Kawahara-RLW equation that describes the dynamics of shallow water waves in oceans and rivers. We confirm that our new algorithm is energy-reserved and unconditionally stable. In order to determine the performance of our numerical algorithm, we have computed the error norms $L_{2}$ and $L_{\infty }$. Convergence of full discrete scheme is firstly studied. Numerical experiments are implemented to validate the energy conservation and effectiveness for longtime simulation. The obtained numerical results have been compared with a study in the literature for similar parameters. This comparison clearly shows that our results are much better than the other results.

Keywords

### History

• Receive Date: 18 September 2018
• Revise Date: 12 November 2018
• Accept Date: 18 November 2018