Numerical simulation and convergence analysis of a high-order conservative difference scheme for SRLW equation

Coupled with the Richardson extrapolation, a new conservative Crank–Nicolson finite difference scheme, which has the accuracy of O(τ²+h⁴)$O({\tau }^2+h^4)$ without refined mesh for the symmetric regularized long wave equation is proposed. The corresponding conservative quantities are discussed, and the existence of numerical solution is proved by the Browder fixed point theorem. The convergence, unconditional stability and uniqueness of the scheme are also derived using the energy method. Numerical results are given to verify the accuracy and the efficiency of proposed algorithm.