Convergence of two conservative high-order accurate difference schemes for the generalized Rosenau–Kawahara-RLW equation

Abstract

In this paper, we present two high-order accurate difference schemes for the generalized Rosenau–Kawahara-RLW equation. The proposed schemes guarantee the conservation of the discrete energy. The unique solvability of the difference solution is proved. A priori error estimates for the numerical solution is derived. Convergence and stability of the difference schemes are proved. The convergence order is $$O(h^{4} + k^{2} )$$ in the uniform norm is discussed without any restrictions on the mesh sizes. Finally, numerical experiments are carried out to support the theoretical claims.