Applied Mathematics and Mechanics

, Volume 28, Issue 9, pp 1181–1189 | Cite as

Multi-symplectic methods for membrane free vibration equation

  • Hu Wei-peng  (胡伟鹏)
  • Deng Zi-chen  (邓子辰)Email author
  • Li Wen-cheng  (李文成)


In this paper, the multi-symplectic formulations of the membrane free vibration equation with periodic boundary conditions in Hamilton space are considered. The complex method is introduced and a semi-implicit twenty-seven-points scheme with certain discrete conservation laws—a multi-symplectic conservation law (CLS), a local energy conservation law (ECL) as well as a local momentum conservation law (MCL)—is constructed to discrete the PDEs that are derived from the membrane free vibration equation. The results of the numerical experiments show that the multi-symplectic scheme has excellent long-time numerical behavior.

Key words

multi-symplectic complex discretization Runge-Kutta methods 

Chinese Library Classification


2000 Mathematics Subject Classification

35Q05 35J05 35J25 


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Copyright information

© Editorial Committee of Appl. Math. Mech. 2007

Authors and Affiliations

  • Hu Wei-peng  (胡伟鹏)
    • 1
  • Deng Zi-chen  (邓子辰)
    • 1
    • 2
    Email author
  • Li Wen-cheng  (李文成)
    • 3
  1. 1.School of Mechanics, Civil Engineering and ArchitectureNorthwestern Polytechnincal UniversityXi’anP. R. China
  2. 2.State Key Laboratory of Structural Analysis of Industrial EquipmentDalian University of TechnologyDalianP. R. China
  3. 3.School of ScienceNorthwestern Polytechnical UniversityXi’anP. R. China

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