线性哈密尔顿系统的m次连续有限元法  

M Order Continuous Finite Element Methods for Linear Hamilton Systems

作　　者：汤琼[1] 陈传淼[2] 刘罗华[1] 

机构地区：[1]湖南工业大学信息与计算科学系,湖南株洲412008 [2]湖南师范大学数学与计算机科学学院,湖南长沙410081

出　　处：《株洲工学院学报》2006年第6期28-31,35,共5页Journal of Zhuzhou Institute of Technology

基　　金：国家自然科学基金资助项目(10471038);湖南省教育厅基金资助项目(05C525)

摘　　要：利用常微分方程的连续有限元法证明了m次连续有限元算法能保持哈密尔顿系统的能量守恒。对线性哈密尔顿系统的m次连续有限元算法为辛算法,且能保持能量守恒,数值例子也验证了此结论。By taking advantages of the continuous finite element methods for ordinary differential equations, the m order finite element methods for linear Hamihonian systems are proved to hold as well as conversation of energy. The method of symplectic algorithm maintains the energy for nonlinear Hamihonian systems. The numerical examples given here are also argees with the theory.

关 键 词：哈密尔顿系统 连续有限元方法 辛算法 能量守恒 

分 类 号：O242[理学—计算数学]