KdV方程的保结构算法

Structure-preserving algorithm for the KdV equation

本文以修正项差分格式(有参数和带参数)为工具,运用保持离散守恒量之条件,尝试求得参数的应有特征,由此推得满足KdV方程离散守恒量标准的半离散差分格式。接着给出此类半离散差分格式上的时间方向可能的离散方式,进而让得到的全离散格式能够保持KdV方程要求的离散守恒量。

in this paper,the modified difference schemes with parameters and with parameters are used to determine the characteristics of parameters by maintaining the conditions of discrete conserved quantities,so as to obtain a semi discrete difference scheme satisfying the discrete conserved quantities of KdV equation.Then,the time direction discretization methods of these semi discrete difference schemes are given,so that the fully discrete schemes still keep the discrete conservation of KdV equation.