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Numerische Mathematik

, Volume 61, Issue 1, pp 501–521 | Cite as

Symplectic phase flow approximation for the numerical integration of canonical systems

  • S. Miesbach
  • H. J. Pesch
Article

Summary

New methods are presented for the numerical integration of ordinary differential equations of the important family of Hamiltonian dynamical systems. These methods preserve the Poincaré invariants and, therefore, mimic relevant qualitative properties of the exact solutions. The methods are based on a Runge-Kutta-type ansatz for the generating function to realize the integration steps by canonical transformations. A fourth-order method is given and its implementation is discussed. Numerical results are presented for the Hénon-Heiles system, which describes the motion of a star in an axisymmetric galaxy.

Mathematics Subject Classification (1991)

65L05 65L07 58F05 70-08 70F15 70H15 

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Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • S. Miesbach
    • 1
  • H. J. Pesch
    • 1
  1. 1.Mathematisches InstitutTechnische Universität MünchenMünchen 2Germany

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