KdV方程的高精度多步显式差分格式

Highly accurate multistep explicit scheme for KdV equation

为提高KdV方程的数值计算精度和效率,提出了一种新的高精度多步显式差分格式.空间坐标按高精度差分法离散,沿时间方向作数值积分,用Largrang插值、构造差商等方法处理网格虚点的值.利用精确解给出初边值条件,利用Matlab软件编程求出数值解,并与指数型差分格式的数值解和解析数值解进行比较.数值结果表明,本文提出的格式具有精度高且计算时间长的优点.

A highly accurate multistep explicit scheme for KdV equation is proposed in order to improve accuracy and efficency. The space derivatives are discretiaed with respect to high accurate difference method,and integration is used on time. Virtual mesh points are valued by Largrang value and scheme difference. Numerical method is obtained. Its initial-boundary value conditions are valued by exact solution. The numerical solution of KdV equation is obtained using Matlab software and compared with that of exponentian scheme and analytical-numerical method. The numerical results show that the scheme of this article has some advantages of high precision and long computing time.