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.
