非线性动力系统的自适应显式Magnus数值方法

doi:10.1007/s10483-008-0901-5

Applied Mathematics and Mechanics (English Edition) ›› 2008, Vol. 29 ›› Issue (9): 1111-1118 .doi: https://doi.org/10.1007/s10483-008-0901-5

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非线性动力系统的自适应显式Magnus数值方法

李文成¹,邓子辰^2,3

1.西北工业大学理学院,西安 710072; 2.西北工业大学力学与土建学院,西安 710072; 3.大连理工大学工业装备结构分析国家重点实验室,辽宁大连 116023

收稿日期:2008-01-24 修回日期:2008-07-13 出版日期:2008-09-10 发布日期:2008-09-10
通讯作者: 邓子辰

Adaptive explicit Magnus numerical method for nonlinear dynamical systems

LI Wen-cheng¹, DENG Zi-chen^2,3

1. School of Science, Northwestern Polytechnical University, Xi'an 710072, P. R. China;
2. Department of Engineering Mechanics, Northwestern Polytechnical University, Xi'an 710072, P. R. China;
3. State Key Laboratory of Structural Analysis of Industrial Equipment, Dalian University of Technology, Dalian 116023, P. R. China

Received:2008-01-24 Revised:2008-07-13 Online:2008-09-10 Published:2008-09-10
Contact: DENG Zi-chen

摘要/Abstract

摘要： 基于最近发展的矩阵李群上非线性微分方程的显式Magnus展式,给出了非线性动力系统的有效的数值算法,并且在数值求解过程中具有自适应的步长控制也点，可以显著地提高计算效率.最后,通过非线性动力学系统典型问题Dugffing方程和强刚性的Van der Pol方程以及非线性振子的Hamilton方程的数值实验来说明方法的有效性.

关键词: 非线性动力系统, Hamilton系统, 数值方法, 步长控制

Abstract: Based on the new explicit Magnusexpansion developed for nonlinear equations defined on a matrix Lie group, an efficient numerical method is proposed for nonlinear dynamical systems. To improve computational efficiency, the integration step size can be adaptively controlled. Validity and effectiveness of the method are shown by application to several nonlinear dynamical systems including the Duffing system, the van der Pol system with strong stiffness, and the nonlinear Hamiltonian pendulum system.

Key words: nonlinear dynamical system, Hamiltonian system, numerical integrator, step size control

中图分类号:

李文成;邓子辰;. 非线性动力系统的自适应显式Magnus数值方法[J]. Applied Mathematics and Mechanics (English Edition), 2008, 29(9): 1111-1118 .

LI Wen-cheng;DENG Zi-chen;. Adaptive explicit Magnus numerical method for nonlinear dynamical systems[J]. Applied Mathematics and Mechanics (English Edition), 2008, 29(9): 1111-1118 .

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非线性动力系统的自适应显式Magnus数值方法

Adaptive explicit Magnus numerical method for nonlinear dynamical systems

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