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.
出处
《计算力学学报》
CAS
CSCD
1999年第3期349-354,共6页
Chinese Journal of Computational Mechanics
关键词
色散方程
高稳定性
显格式
单点精细积分
dispresive equation
higher stability
explicit difference scheme
single point precise integration
