摘要
提出了一族三维热传导方程的两层显式差分格式 ,当截断误差阶为O(Δt +(Δx) 2 )时 ,稳定性条件为网格比r=Δt(Δx) 2 =Δt(Δy) 2 =Δt(Δz) 2 ≤ 12 ,优于其他显式差分格式· 而当截断误差阶为O((Δt) 2 +(Δx) 4 )时 ,稳定性条件为r≤ 1/ 6 ,包含了已有的结果·
A class of two_level explicit difference schemes are presented for solving three_dimensional heat conduction equation. When the order of truncation error is O( Δ t+( Δ x) 2), the stability condition is mesh ratio r= Δ t( Δ x) 2= Δ t( Δ y) 2= Δ t( Δ z) 2≤12, which is better than that of a all the other explicit difference schemes. And when the order of truncation error is O(( Δ t) 2+( Δ x) 4), the stability condition is r≤1/6, which contains the known results.
出处
《应用数学和力学》
EI
CSCD
北大核心
2000年第9期966-972,共7页
Applied Mathematics and Mechanics
基金
福建省自然科学基金资助项目
关键词
三维热传导方程
显式差分格式
截断误差
稳定性
three_dimensional heat conduction equation
explicit difference scheme
truncation error
stability condition
