色散方程的高稳定性三层五点显格式的广义单点精细积分法

A generalized single-point precise integration method of three-level five-point explicit difference schemes with higher stability for dispersion equation

基于文［１］中的单点精细积分方法，对色散方程Ｕｔ＝ ａＵｘｘｘ 提出了一种构造高稳定性三层五点（蛙跳）显格式的广义单点精细积分法．文中格式的局部截断误差为Ｏ（τ２ ＋ ｈ２），而稳定性条件为｜Ｒ｜ ≤ｇ（β）（其中ｇ 对任意正实数是单调递增函数），是同类格式中最好的［２］。

Based on single\|point precise integration method in [1], a generalized single\|point precise integration method of three\|level five\|point explicit difference schemes with high stability for dispersion equation U t=aU xxx is proposed in this paper. Their local truncation errors are O(τ 2+h 2) and stability conditions are｜R｜≤f(β), where f is an increasing function of its variable. f(40)=10 and f(400)=100 etc. These results are much better than｜R｜≤0 3849 in [2] and seem to be the best for schemes of the same type at present.