A new numerical application of the generalized Rosenau-RLW equation

In this article, a collocation finite element method based on septic B-splines as a tool has been carried out to obtain the numerical solutions of the nonlinear generalized Rosenau-RLW equation. One of the advantages of this method is that when the bases are chosen at a high degree, better numerical solutions are obtained. Effectiveness of the method is demonstrated by solving the equation with various initial and boundary conditions. Also, in order to detect the performance of the method we have computed L2 and L1 error norms and two lowest invariants IM and IE: The obtained numerical results have been compared with some of those in the literature for similar parameters. This comparison clearly shows that the obtained results are better than and found in good conformity with the some earlier results. Stability analysis denotes that our algorithm, based on a Crank Nicolson approximation in time, is unconditionally stable.