摘要
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.
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.
基金
Project supported by the National Natural Science Foundation of China (No.10572119)Program for New Century Excellent Talent of Ministry of Education of China (No.NCET-04-0958)the Open Foundation of State Key Laboratory of Structural Analysis of Industrial Equipmentthe Doctorate Foundation of Northwestern Polytechnical University
