A conservative difference scheme with six-order spatial accuracy for the KdV equation

Abstract:

In this paper, we propose a two-level differece scheme with six-order spatial accuracy for the initial boundary value problem of KdV equation with homogeneous boundary condition. In this scheme, the Crank-Nicolson difference scheme with second-order theoretical accuracy in time layer and the discretization of space layer is performed by extrapolating difference combination with six-order accuracy. This scheme can simulate two conservation properties of the original problem reasonably. Then the convergence and stability of the scheme are proved by using the energy method. Finally, numerical examples verify the performance of the scheme.