Study on convergence and stability of a conservative difference scheme for the generalized Rosenau-KdV equation

In this paper, a conservative nonlinear implicit finite difference scheme for the generalized Rosenau-KdV equation is studied. Convergence and stability of the proposed scheme are proved by a discrete energy method. The proof with a priori error estimate shows that the convergence rates of numerical solutions are both the second order on time and in space. Meanwhile, numerical experiments are carried out to verify the theoretical analysis and show that the scheme is efficient and reliable.