|
|||||
|
|
| 代数偏微分方程组的对合特征集方法分析（英文） | |
| 引用本文： | 孟晓辉,陈玉福.代数偏微分方程组的对合特征集方法分析（英文）[J].中国科学院研究生院学报,2006,23(1):7-22. |
| 作者姓名： | 孟晓辉 陈玉福 |
| 作者单位： | 1. 北京市计算中心,北京,100005 2. 中国科学院研究生院,北京,100049 |
| 基金项目： | supported in part by a National Key Basic Research Project of China(G19980306) |
| 摘 要： | 基于Wu-Ritt特征集方法和V.Gerdt的对合除法, 我们定义了非线性偏微分方程组的关于一般延拓方向的对合特征集 (ICS). 影响ICS方法的两个主要因素为: 延拓方向和变量的序. 本文中, 应用ICS方法处理在计算偏微分方程组的对称群过程中产生的大型偏微分方程组. 在实验的基础上, 总结了对于ICS方法较好的延拓方向和变量的序. |
| 关 键 词： | 对合特征集 可积条件 代数偏微分方程组 Wu-Ritt 特征集方法 |
| 文章编号： | 1002-1175(2006)01-0007-16 |
| 修稿时间： | 2005年1月7日 |
Analysis of the Involutive Characteristic Set Method for Algebraic PDE Systems |
|
| MENG Xiao-Hui,CHEN Yu-Fu.Analysis of the Involutive Characteristic Set Method for Algebraic PDE Systems[J].Journal of the Graduate School of the Chinese Academy of Sciences,2006,23(1):7-22. | |
| Authors: | MENG Xiao-Hui CHEN Yu-Fu |
| Institution: | 1 Beijing Municipal Computing Center, Beijing 100005, China; ]
2 Graduate School of the Chinese Academy of Sciences, Beijing 100039, China |
| Abstract: | Based on Wu-Ritt's characteristic set method and V. Gerdet's involutive division method, we defined the involutive characteristic set (ICS) for a set of non-linear PDEs with respect to a general involutive direction. The ICS method depends on two factors: the prolongation direction and the variable ordering. In this paper, we report an implementation of the ICS method and use it to solve a large set of PDE systems raised from the computation of symmetric groups for PDEs. Based on the experiments, we try to select the best prolongation direction and the variable ordering for the ICS algorithm. |
| Keywords: | involutive characteristic set integrability conditions algebraic partial differential equation system Wu-Ritt's characteristic set method |
| 本文献已被 CNKI 万方数据 等数据库收录！ | |
| 点击此处可从《中国科学院研究生院学报》浏览原始摘要信息 | |
| 点击此处可从《中国科学院研究生院学报》下载免费的PDF全文 | |