Authors

O. Gonzalez

Abstract

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.

Keywords

Hamiltonian System; Discrete System; Relative Equilibrium; Symplectic Structure; Reduce Phase Space

Citation

  • Journal: Journal of Nonlinear Science
  • Year: 1996
  • Volume: 6
  • Issue: 5
  • Pages: 449–467
  • Publisher: Springer Science and Business Media LLC
  • DOI: 10.1007/bf02440162

BibTeX

@article{Gonzalez_1996,
  title={{Time integration and discrete Hamiltonian systems}},
  volume={6},
  ISSN={1432-1467},
  DOI={10.1007/bf02440162},
  number={5},
  journal={Journal of Nonlinear Science},
  publisher={Springer Science and Business Media LLC},
  author={Gonzalez, O.},
  year={1996},
  pages={449--467}
}

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