Taylor Polynomial Stepwise Refinement Algorithm for Lie and High Symmetries of Partial Differential Equations

Zhang Hongqing; Tang Limin; Chao Lu

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Article Navigation > Applied Mathematics and Mechanics > 1998 > 19(3): 195-201

Zhang Hongqing, Tang Limin, Chao Lu. Taylor Polynomial Stepwise Refinement Algorithm for Lie and High Symmetries of Partial Differential Equations[J]. Applied Mathematics and Mechanics, 1998, 19(3): 195-201.

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Taylor Polynomial Stepwise Refinement Algorithm for Lie and High Symmetries of Partial Differential Equations

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

Received Date: 1996-07-05
Rev Recd Date: 1997-10-05
Publish Date: 1998-03-15

Abstract

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

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References(7)

References

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