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Efficient numerical integrators for highly oscillatory dynamic systems based on modified magnus integrator method

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Abstract

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 second-order 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

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Authors and Affiliations

  1. School of Science, Northwestern Polytechnical University, Xi’an, 710072, P. R. China

    Li Wen-cheng Doctor  (李文成)

  2. School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi’an, 710072, P. R. China

    Deng Zi-chen  (邓子辰) & Huang Yong-an  (黄永安)

  3. State Key Laboratory of Structural Analysis of Industrial Equipment, Dalian University of Technology, Dalian, 116023, P. R. China

    Deng Zi-chen  (邓子辰)

Authors
  1. Li Wen-cheng Doctor  (李文成)
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  2. Deng Zi-chen  (邓子辰)
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  3. Huang Yong-an  (黄永安)
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Corresponding author

Correspondence to Li Wen-cheng Doctor  (李文成).

Additional information

Communicated by YUE Zhu-feng

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 Equipment and the Doctorate Foundation of Northwestern Polytechnical University

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Li, Wc., Deng, Zc. & Huang, Ya. Efficient numerical integrators for highly oscillatory dynamic systems based on modified magnus integrator method. Appl Math Mech 27, 1383–1390 (2006). https://doi.org/10.1007/s10483-006-1010-z

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  • DOI: https://doi.org/10.1007/s10483-006-1010-z

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2000 Mathematics Subject Classification

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