任意差分精细积分法及数值稳定性分析

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On the Arbitrary Difference Precise Integration Method and Its Numerical Stability

Department of Bridge and Structural Engineering, Southwest Jiaotong University, Chengdu 610031, P. R. China

摘要: 本文在子域精细积分法的基础上,提出解偏微分方程的任意差分精细积分法,这种方法既具备子域精细积分法的各种优点,还能较好描述非均匀介质的物理特性及灵活处理各类边界条件,且其显式计算格式是无条件稳定的.
- 偏微分方程 /
- 差分法 /
- 数值稳定性
Abstract: Based on the subdomain precise integration method, the arbitrary difference precise integration method (ADPIM) is presented to solve PDEs. While retaining all the merits of the former method, ADPIM further demonstrates advantages such as the abilities of better description of physical properties of inhomogeneous media and convenient treatment of various boundary conditions. The explicit integration schemes derived by ADPIM are proved unconditionally stable.
- partial differential equations /
- difference method /
- numerical stability

[1]	Batge K J,Wilson E L.Numerical Methods in Finite Element Analysis[M].Engelwood Chiff,NJ:Prentice-Hall,1976
[2]	Lapidus L,Pinder G F.Numerical Solution of Partial Differential Equations in Science and Engineering[M].John Wiley & Sons,1982
[3]	钟万勰,朱建平.对差分法时程积分的反思[J].应用数学和力学,1995,16(8):663～668
[4]	钟万勰.单点子域积分与差分[J].力学学报,1996,28(2):159～163
[5]	钟万勰.子域精细积分及偏微分方程的数值解[J].计算结构力学及其应用,1995,12(3):253～260
[6]	蔡志勤,钟万勰.子域精细积分的稳定性分析[J].水动力学研究与进展A辑,1995,10(6):588～593
[7]	李光耀,周汉斌.变厚度薄板弯曲问题的任意网格差分解法[J].应用数学和力学,1993,14(3):281～286