Hostname: page-component-848d4c4894-2pzkn Total loading time: 0 Render date: 2024-05-06T15:01:58.207Z Has data issue: false hasContentIssue false
  • English
  • Français

Symplectic Integrators for Hamiltonian Systems: Basic Theory

Published online by Cambridge University Press:  07 August 2017

Haruo Yoshida
Haruo Yoshida*
Affiliation:
National Astronomical Observatory, Mitaka, Tokyo 181, Japan

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Symplectic integrators are numerical integration methods for Hamiltonian systems, which conserves the symplectic 2-form exactly. With use of symplectic integrators there is no secular increase in the error of the energy because of the existence of a conserved quantity closed to the original Hamiltonian. Higher order symplectic integrators are obtained by a composition of 2nd order ones.

Keywords

Numerical integration methodSymplectic mappingConserved quantity
Type
Part VII - Dynamical Systems. Maps. Integrators
Information
Symposium - International Astronomical Union , Volume 152: Chaos, Resonance and Collective Dynamical Phenomena in the Solar System , 1992 , pp. 407 - 411
Copyright
Copyright © Kluwer 1992 

References

Candy, J. and Rozmus, W.: 1991, ‘A symplectic integration algorithm for separable Hamiltonian functions’, J. Comp. Phys. 92, 230 Google Scholar
Channel, P.J. and Scovel, J.C.: 1990, ‘Symplectic integration of Hamiltonian systems’, Nonlinearity 3, 231 CrossRefGoogle Scholar
Forest, E. and Ruth, R.D.: 1990, ‘Fourth-order symplectic integration’, Physica D 43, 105 CrossRefGoogle Scholar
Forest, E., Brengtsson, J. and Reusch, M.F.: 1991, ‘Application of the Yoshida-Ruth techniques to implicit integration and multi-map explicit integration’, Phys. Lett. A 158, 99 CrossRefGoogle Scholar
Kinoshita, H., Yoshida, H. and Nakai, H: 1991, ‘Symplectic integrators and their application to dynamical astronomy’, Celest. Mech. 50, 59 CrossRefGoogle Scholar
Pullin, D.I. and Saffman, P.G.: 1991, ‘Long time symplectic integration, the example of four-vortex motion’, Proc. R. Soc. London A 432, 481 Google Scholar
Yoshida, H: 1990, ‘Construction of higher order symplectic integrators’, Phys. Lett. A 150, 262 Google Scholar