A sixth-order accuracy conservative linear finite difference scheme for RLW equation

By the Taylor expansion and extrapolation combinations in the spatial direction, the second order and fourth order components of spatial truncation errors can be removed, resulting in a theoretical accuracy of sixth order. In the temporal direction, the average implicit method is employed to achieve second-order theoretical accuracy. Subsequently, a linear average implicit difference scheme for the initial boundary value problem of regularized long wave equation is constructed, which can reasonably simulate the two conservative quantities of the problem. Moreover, the convergence and stability of the scheme are also proved. Numerical examples also demonstrate the effectiveness of the proposed method.