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

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

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

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.