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Applied Mathematics and Mechanics (English Edition) ›› 1998, Vol. 19 ›› Issue (3): 213-220.

• 论文 • 上一篇    下一篇

TAYLOR POLYNOMIAL STEPWISE REFINEMENTALGORITHM FOR LIE AND HIGH SYMMETRIES OF PARTIAL DIFFERENTIAL EQUATIONS

张鸿庆1, 朝鲁2, 唐立民3   

  1. 1. Institute of Mathematics, Dalian University of Technology, Dalian 116024. P. R. China;
    2. Basic Science Department, Inner Mongolia Polytechnic University, Huhhot 010062, P. R. China;
    3. Department of Mechanics, Dalian University of Tcchnoloky, Dalian 1 16024, P. R. China
  • 收稿日期:1996-07-05 修回日期:1997-10-05 出版日期:1998-03-18 发布日期:1998-03-18
  • 基金资助:
    Project is supported by the National Natural Science Foundation and MMM Center of China

TAYLOR POLYNOMIAL STEPWISE REFINEMENT ALGORITHM FOR LIE AND HIGH SYMMETRIES OF PARTIAL DIFFERENTIAL EQUATIONS

Zhang Hongqing1, Chao Lu2, Tang Limin3   

  1. 1. Institute of Mathematics, Dalian University of Technology, Dalian 116024. P. R. China;
    2. Basic Science Department, Inner Mongolia Polytechnic University, Huhhot 010062, P. R. China;
    3. Department of Mechanics, Dalian University of Tcchnoloky, Dalian 1 16024, P. R. China
  • Received:1996-07-05 Revised:1997-10-05 Online:1998-03-18 Published:1998-03-18
  • Supported by:
    Project is supported by the National Natural Science Foundation and MMM Center of China

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摘要： In this article,based on the Taylor expansions of generating functions and stepwise refinement procedure,authors suggest a algorithm for finding the Lie and high (generalzed symmetries of partial differential equations (PDEs).This algorithmtransforms the problem having to solve over-determining PDEs,This algorithmand difficulty part in standard methods into one solving to algebaic equations towhich one easy obtain solution,So,it reduces significantly the difficulties of the problem and raise computing efficiency.The whole procedure of the akgorithm is carried out automatically by using any computer algebra system.In geeneral,this algorithm can yields many more important symmetries for PDEs.

关键词: Lie groups, high symmetries, Taylor polynomial, computer algebra, determining equations, stepwise rdfinement.

Abstract: In this article,based on the Taylor expansions of generating functions and stepwise refinement procedure,authors suggest a algorithm for finding the Lie and high (generalzed symmetries of partial differential equations (PDEs).This algorithmtransforms the problem having to solve over-determining PDEs,This algorithmand difficulty part in standard methods into one solving to algebaic equations towhich one easy obtain solution,So,it reduces significantly the difficulties of the problem and raise computing efficiency.The whole procedure of the akgorithm is carried out automatically by using any computer algebra system.In geeneral,this algorithm can yields many more important symmetries for PDEs.

Key words: Lie groups, high symmetries, Taylor polynomial, computer algebra, determining equations, stepwise rdfinement.

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