| Geometric integration methods for general nonlinear dynamic equation based on Magnus and Fer expansions |
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| 作者姓名： | ZHANG Suying DENG Zichen |
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| 作者单位： | Department of Engineering Mechanics, Northwestern Polytechnical University, Xi'an 710072, China;College of Physical Electronic Engineering, Shanxi University, Taiyuan 030006, China,Department of Engineering Mechanics, Northwestern Polytechnical University, Xi'an 710072, China;State Key Laboratory of Structural Analysis of Industrial Equipment,Dalian University of Technology, Dalian 116023, China |
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| 基金项目： | 国家自然科学基金，教育部霍英东教育基金，高等学校博士学科点专项科研项目，the Open Foundation of State Key Laboratory of Structural Analysis of Industrial Equipment |
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| 摘 要： | Based on Magnus or Fer expansion for solving linear differential equation and operator semi-group theory, Lie group integration methods for general nonlinear dynamic equation are studied. Approximate schemes of Magnus type of 4th, 6th and 8th order are constructed which involve only 1, 4 and 10 different commutators, and the time-symmetry properties of the schemes are proved. In the meantime, the integration methods based on Fer expansion are presented. Then by connecting the Fer expansion methods with Magnus expansion methods some techniques are given to simplify the construction of Fer expansion methods. Furthermore time-symmetric integrators of Fer type are constructed. These methods belong to the category of geometric integration methods and can preserve many qualitative properties of the original dynamic system.
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| 关 键 词： | nonlinear dynamic system geometric integration method Lie group method Magnus expansion Fer expa |
Geometric integration methods for general nonlinear dynamic equation based on Magnus and Fer expansions |
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| ZHANG Suying,DENG Zichen.Geometric integration methods for general nonlinear dynamic equation based on Magnus and Fer expansions[J].Progress in Natural Science,2005,15(4):304-314. |
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| Authors: | ZHANG Suying Deng Zichen |
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| Institution: | 1. Department of Engineering Mechanics, Northwestern Polytechnical University, Xi'an 710072, China;College of Physical Electronic Engineering, Shanxi University, Taiyuan 030006, China
2. Department of Engineering Mechanics, Northwestern Polytechnical University, Xi'an 710072, China;State Key Laboratory of Structural Analysis of Industrial Equipment,Dalian University of Technology, Dalian 116023, China |
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| Abstract: | Based on Magnus or Fer expansion for solving linear differential equation and operator semi-group theory, Lie group integration methods for general nonlinear dynamic equation are studied. Approximate schemes of Magnus type of 4th, 6th and 8th order are constructed which involve only 1, 4 and 10 different commutators, and the time-symmetry properties of the schemes are proved. In the meantime, the integration methods based on Fer expansion are presented. Then by connecting the Fer expansion methods with Magnus expansion methods some techniques are given to simplify the construction of Fer expansion methods. Furthermore time-symmetric integrators of Fer type are constructed. These methods belong to the category of geometric integration methods and can preserve many qualitative properties of the original dynamic system. |
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| Keywords: | nonlinear dynamic system geometric integration method Lie group method Magnus expansion Fer expansion |
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