Optimal order and time-step criterion for Aarseth-type N-body integrators
Abstract
How the selection of the time-step criterion and the order of the integrator change the efficiency of Aarseth-type N-body integrators is discussed. An alternative to Aarseth's scheme based on the direct calculation of the time derivative of the force using the Hermite interpolation is compared to Aarseth's scheme, which uses the Newton interpolation to construct the predictor and corrector. How the number of particles in the system changes the behavior of integrators is examined. The Hermite scheme allows a time step twice as large as that for the standard Aarseth scheme for the same accuracy. The calculation cost of the Hermite scheme per time step is roughly twice as much as that of the standard Aarseth scheme. The optimal order of the integrators depends on both the particle number and the accuracy required. The time-step criterion of the standard Aarseth scheme is found to be inapplicable to higher-order integrators, and a more uniformly reliable criterion is proposed.
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Self-citation
- Authors
- Makino, J.
- Corresponding author
- Makino, Junichiro
- ORCID
- Makino, Junichiro
- Venue
- The Astrophysical Journal
- Publisher
- American Astronomical Society
- Published
- 1991-03
- Volume
- 369
- Pages
- 200
- ISSN
- 0004-637X (ISSN-L)
- 1538-4357
- OpenAlex
- W1996792925
- Cited by
- 229
- References
- 0
- Citations by year
- 2026: 8 · 2025: 7 · 2024: 16 · 2023: 8 · 2022: 13 · 2021: 12 · 2020: 7 · 2019: 7 · 2018: 8 · 2017: 9 · 2016: 10 · 2015: 8 · 2014: 14 · 2013: 7 · 2012: 8
- FWCI
- 0.92
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- The Astrophysical Journal (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Numerical Analysis › Numerical Solvers for Ordinary Differential Equations
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Stellar, planetary, and galactic studies
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Galaxies: Formation, Evolution, Phenomena
- Keywords
- Hermite interpolation, Newton interpolation, predictor-corrector method, computational cost, gravitational dynamics, variable time step
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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