KdV方程的对数型有限差分格式

Logarithm finite-difference scheme applied to KdV equation

给出了KdV方程的对数型有限差分格式,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进行比较.结果表明,对数型有限差分格式具有精度高且可以长时间稳定计算的优点.

Logarithm finite-difference scheme applied to Korteweg-de Vries equation is given. It＇ s initial-boundary value conditions are valued by exact solution. Numerical solution of KdV equation using Maflab software is given and the numerical solution of logarithm finite-difference scheme is compared with that of exponentian scheme. The numerical result shows that the scheme of this article has some advantages such as high precision and long computering time.