High-order conservative Crank-Nicolson scheme for regularized long wave equation

Numerical solution for the regularized long wave equation is studied by a new conservative Crank-Nicolson finite difference scheme. By the Richardson extrapolation technique, the scheme has the accuracy of O(tau(2) + h(4)) without refined mesh. Conservations of discrete mass and discrete energy are discussed, and existence of the numerical solution is proved by the Browder fixed point theorem. Convergence, unconditional stability as well as uniqueness of the solution are also derived using energy method. Numerical examples are carried out to verify the correction of the theory analysis.