摘要
构造了一族三维抛物型方程的两层显格式。证明了当截断误差阶为O(Δt+Δx2 )时 ,其稳定性条件为网比 r =Δt/Δx2 =Δt/Δy2 =Δt/Δz2 ≤ 1/ 2 ,优于同类的其他显格式。当截断误差阶为O(Δt2 +Δx4)时 ,此格式为一个简洁而实用的高精度两层显格式。
A class of two level explicit difference schemes are presented for solving three dimensional parabolic equations. When the order of truncation error is O( Δ t+ Δ x 2), the stability condition is mesh ratir r= Δ t Δ x 2= Δ t Δ y 2= Δ t Δ z 212, which is better than that of all the other explicit difference schemes. And when the order of truncation error is O( Δ t 2+ Δ x 4), it becomes a concise and practical two level explicit scheme with high accuracy.
出处
《工程数学学报》
CSCD
北大核心
2002年第1期139-142,共4页
Chinese Journal of Engineering Mathematics
基金
河南省教委自然科学基础研究项目
关键词
三维抛物型方程
显式差分格式
截断误差
稳定性
Three dimensional parabolic equations
Explicit difference schemes
Truncation error
Stability
