A High-order Nonlinear Conserved C-N Differential Scheme for the RLW-KdV Equation

A new high-order nonlinear conservative difference scheme was proposed for the initial boundary value problems of the RLW equation. The Taylor expansion and the partial extrapolation were used to make the second-order term of the truncation error be removed directly at the spatial layer, and the Crank- Nicolson scheme was adopted at the temporal layer, which results in second-order and fourth-order ac-curacy in the temporal and spatial directions, respectively, and reasonably simulates a conserved quantity of the problem itself. The convergence and stability of this scheme were proved by discrete Sobolev embedding inequality and the discrete functional analysis method, and the results of the numerical example experiments verify that the method is feasible.