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Symplectic integration of Hamiltonian systems
Open accessAbstract
The authors survey past work and present new algorithms to numerically integrate the trajectories of Hamiltonian dynamical systems. These algorithms exactly preserve the symplectic 2-form, i.e. they preserve all the Poincare invariants. The algorithms have been tested on a variety of examples and results are presented for the Fermi-Pasta-Ulam nonlinear string, the Henon-Heiles system, a four-vortex problem, and the geodesic flow on a manifold of constant negative curvature. In all cases the algorithms possess long-time stability and preserve global geometrical structures in phase space.
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Citations
Cited by
Construction of higher order symplectic integrators
Yoshida, H. (1990) · Physics Letters A · doi:10.1016/0375-9601(90)90092-3 · Cited by 2,289
Quantum Algorithms for Quantum Chemistry and Quantum Materials Science
Bauer, B., Bravyi, S., Motta, M., & Chan, G. K.-L. (2020) · Chemical Reviews · doi:10.1021/acs.chemrev.9b00829 · Cited by 848
Numerical integration of ordinary differential equations on manifolds
Crouch, P. E., & Grossman, R. (1993) · Journal of Nonlinear Science · doi:10.1007/bf02429858 · Cited by 334
Metadata
- Authors
- Channell, P. J., & Scovel, C.
- Venue
- Nonlinearity
- Publisher
- IOP Publishing
- Published
- 1990-05-01
- Volume
- 3
- Issue
- 2
- Pages
- 231-259
- ISSN
- 0951-7715 (ISSN-L)
- 1361-6544
- OpenAlex
- W2045701663
- Cited by
- 435
- References
- 0
- FWCI
- 30.32
- Type
- journal article
- Language
- en
- Open access
- bronze
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- CoChat. (2026). Citation check: Symplectic integration of Hamiltonian systems. https://app.cochat.ai/papers/10.1088/0951-7715/3/2/001
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- Channell, P. J., & Scovel, C. (1990). Symplectic integration of Hamiltonian systems. Nonlinearity. https://doi.org/10.1088/0951-7715/3/2/001
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
