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启示性方法用于分析有限差分方程的计算稳定性(英文)

  • 肖存英 ,
  • 胡雄
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  • 1. 中国科学院空间科学与应用研究中心,北京,100080;
    2. 中国科学院武汉物理与数学研究所, 武汉,430071;
    3. 中国科学院研究生院,北京,100080

收稿日期: 1900-01-01

  修回日期: 1900-01-01

  网络出版日期: 2007-03-15

Heuristic method approach to the computational stability analysis of finite-dfference equations

  • XIAO Cun-Ying ,
  • HU Xiong
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  • 1.Center for Space Science and Applied Research, Chinese Academy of Science, Beijing 100080, China;
    2. Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071,China;
    3.Graduate University of the Chinese Academy of Sciences, Beijing 100080, China

Received date: 1900-01-01

  Revised date: 1900-01-01

  Online published: 2007-03-15

摘要

这篇文章通过一些典型例子讨论了在用启示性方法时从原偏微分方程推导来的稳定性条件与从差分方程展开式推导来的稳定性条件间的不同点。结果表明,对于部分有限差分方程,在用启示性方法分析其计算稳定性的过程中最好采用从差分方程推导来的展开式以期得到较合理的结果。在文章的另一部分,反证法的运用表明了从启示性方法推导来的稳定性条件并非全都是必要条件,在应用中应引起注意。

本文引用格式

肖存英 , 胡雄 .

启示性方法用于分析有限差分方程的计算稳定性(英文)

[J]. 中国科学院大学学报, 2007 , 24(2) : 179 -185 . DOI: 10.7523/j.issn.2095-6134.2007.2.007

Abstract

Some representative examples are adopted in this paper to discuss the differences between the stability conditions deduced from the original partial differential equations and that obtained from the expansion equations. It shows that for some difference equations, we’d better adopt the expansion equations in the process of the heuristic method being applied to these difference equations. In another part, apagoge is used in this paper to tell us that not all the stability conditions deduced by the heuristic method are the necessary computational stability conditions, which should be pay attention to in their applications.
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