中文摘要：

本文基于经典的有限差分方法，讨论了满足周期边界条件的KdV方程的高精度差分格式的构造问题．通过引入中间函数及紧致方法对空间区域进行离散，提出了KdV方程的一个两层隐式紧致差分格式．利用泰勒展开法得出，该格式在时间方向具有二阶精度，但在空间方向可达到六阶精度．采用线性稳定性分析法证明了该格式是稳定的．数值结果表明：本文所提出的紧致差分格式是有效的，在空间方向拥有较高的精度，还能够很好地保持离散动量和能量守恒性质．

英文摘要：

Based on the classical finite difference method, the paper discusses the construction of a high accuracy difference scheme for the KdV equation with periodic boundary conditions. By introducing an intermediate function and a compact method to discretize the space area, a two-layer implicit compact difference scheme for the KdV equation is proposed. Using the Taylor expansion method, we show that the proposed scheme has second order accuracy in time direction, but can reach sixth order accuracy in spatial direction. The linear stability analysis method proves the scheme is stable. Numerical results show that the compact difference scheme proposed in this paper is effective, it has high accuracy in the spatial direction, and can also keep the conservations of momentum and energy well.