Abstract:
In this study, we have got numerical solutions of the generalized RosenauKdV equation by using collocation finite element method in which septic B-splines are used as
approximate functions. Effectivity and proficiency of the method are shown by solving the
equation with different initial and boundary conditions. Also, to do this L and L 2 error
norms and two lowest invariants MI and EI have been computed. A linear stability analysis
indicates that our algorithm, based on a Crank Nicolson approximation in time, is
unconditionally stable. An error analysis of the new algorithm has been made. The obtained numerical solutions are compared with some earlier studies. This comparison clearly indicates that the obtained results are better than the earlier results.
