KdV方程的一个空间六阶空间精度守恒差分格式

本文对含齐次边界条件的KdV方程的初边值问题进行了数值研究. 通过在时间层进行二阶精度的Crank-Nicolson差分离散、在空间层进行六阶理论精度的外推组合差分离散，本文建立了一个具有六阶空间精度的两层非线性差分格式. 该格式能够合理地模拟原问题的两个守恒量. 然后，本文利用能量方法证明了格式的收敛性和稳定性. 数值算例验证了该方法的有效性.

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

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.