| Structure-Preserving Algorithms for a Class of Dynamical Systems |
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| 作者姓名： | Ling-shu Wang Guang-hui Feng |
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| 作者单位： | [1]School of Mathematics and Statistics, Hebei University of Economics ＆ Business, Shijiazhang 050061, China [2]Mechanical Engineering College, Shijiazhuang 050003, China |
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| 基金项目： | Acknowledgements. We would like to thank Geng Sun, Zai-jiu Shang and Ya-juan Sun for valuable discussions. |
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| 摘 要： | In this paper,we study structure-preserving algorithms for dynamical systems defined by ordinarydifferential equations in R~n.The equations are assumed to be of the form y~·=A(y) D(y) R(y),where A(y)is the conservative part subject to
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| 关 键 词： | SRK法 数字实验 反向误差分析 结构保存算法 动态系统 |
| 收稿时间： | 1 March 2006 |
| 修稿时间： | 2006-03-012006-05-24 |
Structure-Preserving Algorithms for a Class of Dynamical Systems |
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| Ling-shu Wang Guang-hui Feng.Structure-Preserving Algorithms for a Class of Dynamical Systems[J].Acta Mathematicae Applicatae Sinica,2007,23(1):161-176. |
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| Authors: | Ling-shu Wang Guang-hui Feng |
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| Institution: | (1) School of Mathematics and Statistics, Hebei University of Economics & Business, Shijiazhang 050061, China;(2) Mechanical Engineering College, Shijiazhuang 050003, China |
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| Abstract: | Abstract
In this paper, we study structure-preserving algorithms for dynamical systems defined by ordinary differential equations in
R
n
. The equations are assumed to be of the form ẏ = A(y)+D(y) +R(y), where A(y) is the conservative part subject to 〈A(y), y〉 = 0; D(y) is the damping part or the part describing the coexistence of damping and expanding; R(y) reflects strange phenomenon of the system. It is shown that the numerical solutions generated by the symplectic Runge-Kutta(SRK)
methods with b
i
> 0 ( i = 1, • • • , s) have long-time approximations to the exact ones, and these methods can describe the structural properties of the quadratic
energy for these systems. Some numerical experiments and backward error analysis also show that these methods are better than
other methods including the general algebraically stable Runge-Kutta(RK)methods. |
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| Keywords: | SRK methods numerical experiment backward error analysis |
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