Numerical analysis of two new three-point conservative compact difference schemes based on reduction method for solving RLW equation

In this paper, we construct two new three-point conservative compact difference schemes based on the reduction method for solving the regularized long wave (RLW) equation. These schemes have the accuracy of second order in temporal direction and fourth order in spatial direction, and preserve the discrete mass and energy. Boundedness, unique solvability and error estimate of the proposed compact difference schemes are rigorously analysed by using the discrete energy method. Numerical examples are carried out to verify the reliability of the theory analysis.