Analysis of the Involutive Characteristic Set Method for Algebraic PDE Systems

doi:10.7523/j.issn.2095-6134.2006.1.004

›› 2006, Vol. 23 ›› Issue (1): 7-22.DOI: 10.7523/j.issn.2095-6134.2006.1.004

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Analysis of the Involutive Characteristic Set Method for Algebraic PDE Systems

MENG Xiao-Hui，CHEN Yu-Fu

1 Beijing Municipal Computing Center, Beijing 100005, China; ]

2 Graduate School of the Chinese Academy of Sciences, Beijing 100039, China

Received:1900-01-01 Revised:1900-01-01 Online:2006-01-15

Abstract

Abstract: Based onWu-Ritt’s characteristic set method and V. Gerdet’s involutive division method,
we defined the involutive characteristic set (abbr. 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.

Key words: Involutive characteristic set, integrability conditions, algebraic partial differential equation system, Wu-Ritt’s characteristic set method

CLC Number:

MENG Xiao-Hui，CHEN Yu-Fu. Analysis of the Involutive Characteristic Set Method for Algebraic PDE Systems[J]. , 2006, 23(1): 7-22.

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Analysis of the Involutive Characteristic Set Method for Algebraic PDE Systems

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