New conservative difference schemes with fourth-order accuracy for some model equation for nonlinear dispersive waves

In this article, some high-order accurate difference schemes of dispersive shallow water waves with Rosenau-KdV-RLW-equation are presented. The corresponding conservative quantities are discussed. Existence of the numerical solution has been shown. A priori estimates, convergence, uniqueness, and stability of the difference schemes are proved. The convergence order is O(h(4) + k(2)) in the uniform norm without any restrictions on the mesh sizes. At last numerical results are given to support the theoretical analysis.