A numerical study using finite element method for generalized RosenauKawaharaRLW equation

In this paper, we are going to obtain the soliton solution of the generalized RosenauKawaharaRLW equation that describes the dynamics of shallow water waves in oceans and rivers. We confirm that our new algorithm is energyreserved 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.