Adaptive explicit Magnus numerical method for nonlinear dynamical systems  

作　　者：李文成 邓子辰 

机构地区：[1]School of Science,Northwestern Polytechnical University [2]Department of Engineering Mechanics,Northwestern Polytechnical University

出　　处：《Applied Mathematics and Mechanics(English Edition)》2008年第9期1111-1118,共8页应用数学和力学（英文版）

基　　金：the National Natural Science Foundation of China (No. 10632030 and10572119);the Fundamental Research Foundation of NPU;the Scientific and Technological Innovation Foundation for teachers of NPU

摘　　要：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.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.

关 键 词：nonlinear dynamical system Hamiltonian system numerical integrator step size control 

分 类 号：O175[理学—数学]