色散方程的高稳定性两层四点显格式的单点精细积分法  

A single point precise integration method of two level four point explicit difference schemes with higher stability for dispresive equation

作　　者：田振夫[1,2] 张艳萍[1,2] 

机构地区：[1]宁夏大学应用数学研究所 [2]郑州大学建筑工程学院

出　　处：《计算力学学报》1999年第3期349-354,共6页Chinese Journal of Computational Mechanics

摘　　要：基于单点精细积分的思想，对色散方程Ｕｔ＝ａＵｘｘｘ构造了一类高稳定性的两层四点显式差分格式，其局部截断误差为Ｏ（τ＋ｈ），稳定性条件为｜Ｒ｜＝｜ａτ／ｈ３｜≤ｆ（β），其中ｆ（β）对任意正实数β为单调递增函数。它们不仅显著地改善了同类格式的稳定性条件｜Ｒ｜≤０．２５，而且也优于众多三层多点（５点或５点以上）显格式的稳定性条件。Based on single point precise integration method, a class of two level four point explicit difference schemes with higher stability for dispresive equation U t=aU xxx is established in this paper. Their local truncation errors are O(τ+h) and stability conditions are |R|≤f(β), where f is an increasing function of its variable. For example, f(0.1)=0.262708,f(2)=0.575258,f(10)=2.50013 and f(100)=20 etc. These results are much better than |R|≤0.25 in and seem to be the best for schemes of the same type at present.

关 键 词：色散方程 高稳定性 显格式 单点精细积分 

分 类 号：O241.82[理学—计算数学]