代数偏微分方程组的对合特征集方法分析(英文)  

Analysis of the Involutive Characteristic Set Method for Algebraic PDE Systems

作　　者：孟晓辉[1] 陈玉福[2] 

机构地区：[1]北京市计算中心,北京100005 [2]中国科学院研究生院,北京100049

出　　处：《中国科学院研究生院学报》2006年第1期7-22,共16页Journal of the Graduate School of the Chinese Academy of Sciences

基　　金：supportedinpartbyaNationalKeyBasicResearchProjectofChina(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.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.

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 

分 类 号：O175.29[理学—数学] TP391.41[理学—基础数学]