EFFICIENT NUMERICAL INTEGRATORS FOR HIGHLY OSCILLATORY DYNAMIC SYSTEMS BASED ON MODIFIED MAGNUS INTEGRATOR METHOD

• Published in: Applied mathematics and mechanics Vol. 27; no. 10; pp. 1383 - 1390
• Main Author: 李文成 邓子辰 黄永安
• Format: Journal Article
• Language: English
• Published: State Key Laboratory of Structural Analysis of Industrial Equipment,Dalian University of Technology,Dalian 116023,P.R.China%School of Mechanics,Civil Engineering and Architecture,Northwestern Polytechnical University,Xi'an 710072,P.R.China 01.10.2006; School of Science,Northwestern Polytechnical University,Xi'an 710072,P.R.China%School of Mechanics,Civil Engineering and Architecture,Northwestern Polytechnical University,Xi'an 710072,P.R.China
• Subjects: Dynamical systems; Dynamics; Hamiltonian系统; High frequencies; Integrators; Linearization; Magnus积分法; Mathematical analysis; Mathematical models; 动态系统; 非线性振动; Hamiltonian systems; highly oscillatory; Magnus integrator method; dynamic systems
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/s10483-006-1010-z

Based on the Magnus integrator method established in linear dynamic systems, an efficiently improved modified Magnus integrator method was proposed for the second-order dynamic systems with time-dependent high frequencies. Firstly, the secondorder dynamic system was reformulated as the first-order system and the frame of reference was transfered by introducing new variables so that highly oscillatory behaviour inherits from the entries in the meantime. Then the modified Magnus integrator method based on local linearization was appropriately designed for solving the above new form and some improved also were presented. Finally, numerical examples show that the proposed methods appear to be quite adequate for integration for highly oscillatory dynamic systems including Hamiltonian systems problem with long time and effectiveness.