Numerische Mathematik

, Volume 77, Issue 2, pp 269–282 | Cite as

Orthosymplectic integration of linear Hamiltonian systems

  • Benedict J. Leimkuhler
  • Erik S. Van Vleck


The authors describe a continuous, orthogonal and symplectic factorization procedure for integrating unstable linear Hamiltonian systems. The method relies on the development of an orthogonal, symplectic change of variables to block triangular Hamiltonian form. Integration is thus carried out within the class of linear Hamiltonian systems. Use of an appropriate timestepping strategy ensures that the symplectic pairing of eigenvalues is automatically preserved. For long-term integrations, as are needed in the calculation of Lyapunov exponents, the favorable qualitative properties of such a symplectic framework can be expected to yield improved estimates. The method is illustrated and compared with other techniques in numerical experiments on the Hénon-Heiles and spatially discretized Sine-Gordon equations.

Mathematics Subject Classification (1991):65L05 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Benedict J. Leimkuhler
    • 1
  • Erik S. Van Vleck
    • 2
  1. 1. Department of Mathematics, University of Kansas, Lawrence, KS 66045, USA US
  2. 2. Department of Mathematical and Computer Sciences, Colorado School of Mines, Golden, CO 80401, USA US

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