The DOI matches its Crossref record; 13 of the 13 references it cites were found in a registry or an index.
High order symplectic integrators for perturbed Hamiltonian systems
Open accessAbstract
A family of symplectic integrators adapted for the integration of perturbed Hamiltonian systems of the form H = A + εB was given in (McLachlan, 1995). We give here a constructive proof that for all integer p, such integrator exists, with only positive steps, and with a remainder of order O(τpε + τ2ε2), where τ is the stepsize of the integrator. Moreover, we compute the analytical expressions of the leading terms of the remainders at all orders. We show also that for a large class of systems, a corrector step can be performed such that the remainder becomes O(τpε +τ4ε2). The performances of these integrators are compared for the simple pendulum and the planetary three-body problem of Sun–Jupiter–Saturn.
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Cites
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A Multiple Time Step Symplectic Algorithm for Integrating Close Encounters
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General theory of higher-order decomposition of exponential operators and symplectic integrators
Suzuki, M. (1992) · Physics Letters A · doi:10.1016/0375-9601(92)90335-j · Cited by 244
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Self-citationLong term evolution and chaotic diffusion of the insolation quantities of Mars
Laskar, J., Correia, A. C. M., Gastineau, M., Joutel, F., Levrard, B., & Robutel, P. (2004) · Icarus · doi:10.1016/j.icarus.2004.04.005 · Cited by 992
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Anglada-Escudé, G., Tuomi, M., Gerlach, E., Barnes, R., Heller, R., Jenkins, J. S., Wende, S., Vogt, S. S., Paul Butler, R., Reiners, A., et al. (2013) · Astronomy & Astrophysics · doi:10.1051/0004-6361/201321331 · Cited by 381
Omelyan, I. P., Mryglod, I. M., & Folk, R. (2003) · Computer Physics Communications · doi:10.1016/s0010-4655(02)00754-3 · Cited by 254
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Metadata
- Authors
- Laskar, J., & Robutel, P.
- Venue
- Celestial Mechanics and Dynamical Astronomy
- Published
- 2001-05
- Volume
- 80
- Issue
- 1
- Pages
- 39-62
- ISSN
- 0923-2958 (ISSN-L)
- 1572-9478
- OpenAlex
- W1749808203
- Cited by
- 318
- References
- 13
- FWCI
- 5.74
- Type
- journal article
- Language
- en
- Open access
- green
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