Adaptive explicit Magnus numerical method for nonlinear dynamical systems

• Published in: Applied mathematics and mechanics Vol. 29; no. 9; pp. 1111 - 1118
• Main Author: 李文成 邓子辰
• Format: Journal Article
• Language: English
• Published: Heidelberg Shanghai University Press 01.09.2008; State Key Laboratory of Structural Analysis of Industrial Equipment,Dalian University of Technology,Dalian 116023,P.R.China; School of Science,Northwestern Polytechnical University,Xi'an 710072,P.R.China%Department of Engineering Mechanics,Northwestern Polytechnical University,Xi'an 710072,P.R.China
• Subjects: Applications of Mathematics; Classical Mechanics; Computational efficiency; Dynamical systems; Fluid- and Aerodynamics; Lie groups; Mathematical Modeling and Industrial Mathematics; Mathematical models; Mathematics; Mathematics and Statistics; Nonlinear dynamics; Nonlinear equations; Nonlinearity; Numerical analysis; Partial Differential Equations; 动力学系统; 哈密尔敦函数; 数值积分器; 数学分析; nonlinear dynamical system; O322; numerical integrator; 34A26; O241; Hamiltonian system; step size control
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/s10483-008-0901-5

Based on the new explicit Magnus expansion 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.