偏微分方程组的Lie群与高阶对称群的Taylor多项式逐步精化算法<sup>*</sup>

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名

邮箱

手机号码

标题

留言内容

验证码

偏微分方程组的Lie群与高阶对称群的Taylor多项式逐步精化算法^*

基金项目: * 国家自然科学基金及数学机械化中心资助项目

1.
Institute of Mathematics, Dalian Univ, of Tech., Dalian 116024, P. R. China;
2.
Basic Science Department of Inner Mongolia Polyt. Univ., Huhhot 010062, P. R. China;
3.
Department of Mechanics, Dalian Univ of Tech., Dalian 116024, P. R. China

摘要: 本文基于生成函数的Taylor展开式及逐步简化步骤,提出了计算偏微分方程组的Lie群与高阶对称群的Taylor多项式算法,把标准算法中的求解超定偏微分方程组的问题转化为求解代数方程组的问题,降低了求解的难度,提高了计算效率,并且易用计算机代数系统在计算机上全过程实现,并得到重要的对称群.
- Lie群 /
- 高阶对称群 /
- Taylor多项式 /
- 计算机代数 /
- 确定方程 /
- 逐步精化法
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(generalized)symmetries of partial differential equations(PDEs).This algorithm transforms the problem having to solve over-determining PDEs commonly encountered and difficulty part in standard methods into one solving to algebraic equations to which one easy obtain solution.So,it reduces significantly the difficulties of the problem and raise computing efficiency.The whole procedure of the algorithm is carried out automatically by using any computer algebra system.In general,this algorithm can yields many more important symmetries for PDEs.
- Lie groups /
- high symmetries /
- Taylor polynomial /
- computer algebra /
- determining equations /
- stepwise refinement

[1]	P.J.Olver,Applications of Lie Groups to Differential Equations,Springer-Verlag,New York,Berlin,Heideberg,Tokyo(1986).
[2]	R.O.Weber and S.I.Barry,Finite-time blow-up in reaction diffiusion equations,Math.Comput.Modelling,18(10)(1993),163-168.
[3]	Robert Floreanini and Luc.Vinet,Lie symmetries of finite-difference equations,J.Math.Phys.,36(12),(1995).
[4]	F.Schwtz,Automatically determining symmetries of differential equations,Computing,74(1985),91-106.
[5]	G.Bluman and S.Kumei,Symmetries and Differential Equations,Springer-Verlag,New York,Berlin,Heideberg,Tokyo(1989).
[6]	L.V.Ovsiannikov,Group Analysis of Differential Equations,Academic Press,New York(1982).
[7]	沈凤仙,《"Mathematica" 使用手册》,海洋出版社(1991).