摘要
分别从推广的微分方程幂级数解的理论和线性算子半群理论等不同的角度研究了非线性动力学方程的求解问题,得到了所谓的李级数解法.并进一步讨论了算法的具体实施过程,它可以用于构造非线性动力学方程任意高阶的显式积分格式.最后,把李级数解法应用于求解广义Hamilton系统,它能保持广义Hamilton系统真解的典则性.数值算例显示该方法是有效的.
By expanding the power series solution of differential equations and using the semiqroups theory of Linear Operators, we studied the integration method of nonlinear dynamic equations and obtained the so-called Lie series method, whose concrete implementation was discussed. The Lie series method can be used to construct high order explicit Integra tors, so it was used to solve the generalized Hamilton system and it can preserve the canonical property of the exact solution of the generalized Hamilton system. Numerical examples show the method's validity and effectiveness.
出处
《动力学与控制学报》
2004年第1期13-20,共8页
Journal of Dynamics and Control
基金
国家自然科学基金资助项目(10372084)霍英东青年教师基金(71005)高校博士点专项基金(20010699016)大连理工大学工业装备结构分析国家重点实验室开放基金及西北工业大学博士创新基金资助项目~~
关键词
非线性动力学方程
李级数
微分算子
预解式
nonlinear dynamic equation, Lie series,differential operator,the resolvent of the differential operator
