Adaptive explicit Magnus numerical method for nonlinear dynamical systems |
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| Authors: | Wen-cheng Li Zi-chen Deng |
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| Affiliation: | 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;State Key Laboratory of Structural Analysis of Industrial Equipment,Dalian University of Technology,Dalian 116023,P.R.China |
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| Abstract: | 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. |
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| Keywords: | nonlinear dynamical system Hamiltonian system numerical integrator step size control |
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