| 常微方程组初值问题的连续有限元及守恒性 |
| |
| 引用本文： | 刘罗华,汤琼,杨禄源. 常微方程组初值问题的连续有限元及守恒性[J]. 高等学校计算数学学报, 2005, 27(2): 178-184 |
| |
| 作者姓名： | 刘罗华 汤琼 杨禄源 |
| |
| 作者单位： | 株洲工学院信息与计算科学系,株洲,412008;株洲工学院信息与计算科学系,株洲,412008/湖南师范大学数学与计算机科学学院,长沙,410081 |
| |
| 摘 要： | In this paper the continous finite element to solve initinal value problem for system of linear differential equations is used, and the absolute stability of the corresponding single step k-order hidden shceme is discussed. In the paper by simplified means, the superconvergence of finite element and one of it on the nodes are proved. Using the continuous finite element to solve linear Hamilton systems: Pt = Hq，qt = -Hp, the conservation of energy H(p,q) = 1/2 ap^2 bpq 1/2 cq^2 can be obtained. The computation shows that even if division is regular and the error of finite element Ph, qh is big, H(ph, qh) is almost equal H(p, q) in the range of computation accuracy.
|
| 关 键 词： | 常微方程组 初值问题 连续有限元法 守恒性 |
CONTINUOUS FINITE ELEMENT AND ITS CONSERVATION FOR INITIAL VALUE PROBLEM FOR A SYSTEM OF ORDINARY DIFFERENTIAL EQUATIONS |
| |
| Liu Luohua,TANG Qiong,Yang Luyuan. CONTINUOUS FINITE ELEMENT AND ITS CONSERVATION FOR INITIAL VALUE PROBLEM FOR A SYSTEM OF ORDINARY DIFFERENTIAL EQUATIONS[J]. Numerical Mathematics A Journal of Chinese Universities, 2005, 27(2): 178-184 |
| |
| Authors: | Liu Luohua TANG Qiong Yang Luyuan |
| |
| Abstract: | In this paper the continous finite element to solve initinal value problem for system of linear differential equations is used, and the absolute stability of the corresponding single step k-order hidden shceme is discussed. In the paper by simplified means, the superconvergence of finite element and one of it on the nodes are proved. Using the continuous finite element to solve linear Hamilton systems: pt = Hq,qt =-Hp, the conservation of energy H(p,q) = -1/2ap2 + bpq +1/2cq2 can be obtained. The computation shows that even if division is regular and the error of finite element ph,qh is big, H(ph,qh) is almost equal H(p,q) in the range of computation accuracy. |
| |
| Keywords: | systyem of ordinary differential equation continuous finite element superconvergence Hamilton system conservation. |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ |
|
