A detailed numerical study on generalized ROSENAU-KDV equation with finite element method

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