Numerical solution of Rosenau-KdV equation using subdomain finite element method

In this paper, a numerical solution of the Rosenau-Korteweg-de Vries (Rosenau-KdV) equation, based on subdomain method using sextic B-spline is utilized to simulate the motion of single solitary wave. The two invariants of the motion are worked out to define the conservation properties. $L_{2}$ and $L_{infty}$ error norms are used to measure differences between the analytical and numerical solutions. Applying the von-Neumann stability analysis, the proposed method is illustrated to be unconditionally stable. The method is applied on three test examples, and the computed numerical solutions are in good agreement with the result available in literature as well as with exact solutions. The numerical results depict that the scheme is efficient and feasible.