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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） | |
| 引用本文： | 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].中国科学院研究生院学报,2007,24(2):179-185. |
| 作者姓名： | 肖存英 胡雄 |
| 作者单位： | 1. 中国科学院空间科学与应用研究中心,北京,100080;中国科学院武汉物理与数学研究所,武汉,430071;中国科学院研究生院,北京,100080 2. 中国科学院空间科学与应用研究中心,北京,100080 |
| 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。 |
| 关 键 词： | 启示性方法 差分方程 计算稳定性 |
| 文章编号： | 1002-1175(2007)02-0179-07 |
| 修稿时间： | 2006年6月12日 |
Heuristic method approach to the computational stability analysis of finite-dfference equations |
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| XIAO Cun-Ying,HU Xiong.Heuristic method approach to the computational stability analysis of finite-dfference equations[J].Journal of the Graduate School of the Chinese Academy of Sciences,2007,24(2):179-185. | |
| Authors: | XIAO Cun-Ying HU Xiong |
| Institution: | 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 |
| 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 given attention in their applications. |
| Keywords: | heuristic method finite-difference equation computational stability |
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