Journal of Nonlinear Science

, 6:449 | Cite as

Time integration and discrete Hamiltonian systems

  • O. Gonzalez
Article

Summary

This paper develops a formalism for the design of conserving time-integration schemes for Hamiltonian systems with symmetry. The main result is that, through the introduction of a discrete directional derivative, implicit second-order conserving schemes can be constructed for general systems which preserve the Hamiltonian along with a certain class of other first integrals arising from affine symmetries. Discrete Hamiltonian systems are introduced as formal abstractions of conserving schemes and are analyzed within the context of discrete dynamical systems; in particular, various symmetry and stability properties are investigated.

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Copyright information

© Springer-Verlag New York Inc. 1996

Authors and Affiliations

  • O. Gonzalez
    • 1
  1. 1.Division of Applied Mechanics, Department of Mechanical EngineeringStanford UniversityStanfordUSA

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