A new numerical application of the generalized Rosenau-RLW equation

Abstract

. This study implemented a collocation nite element method based on septic B-splines as a tool to obtain the numerical solutions of the nonlinear generalized RosenauRLW equation. One of the advantages of this method is that when the bases are chosen at a high degree, better numerical solutions are obtained. E ectiveness of the method is demonstrated by solving the equation with various initial and boundary conditions. Further, in order to detect the performance of the method, L2 and L1 error norms and two lowest invariants IM and IE were computed. The obtained numerical results were compared with some of those in the literature for similar parameters. This comparison clearly shows that the obtained results are better than and in good conformity with some of the earlier results. Stability analysis demonstrates that the proposed algorithm, based on a Crank Nicolson approximation in time, is unconditionally stable.