Revisiting high-order Taylor methods for astrodynamics and celestial mechanics

ABSTRACT We present heyoka, a new, modern and general-purpose implementation of Taylor’s integration method for the numerical solution of ordinary differential equations. Detailed numerical tests focused on difficult high-precision gravitational problems in astrodynamics and celestial mechanics show...

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Bibliographic Details
Published inMonthly notices of the Royal Astronomical Society Vol. 504; no. 2; pp. 2614 - 2628
Main Authors Biscani, Francesco, Izzo, Dario
Format Journal Article
LanguageEnglish
Published London Oxford University Press 01.06.2021
Subjects
Accuracy
Astrodynamics
Celestial mechanics
Differential equations
Energy conservation law
Integrators
Planetary systems
gravitation
methods: numerical
celestial mechanics
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Summary:ABSTRACT We present heyoka, a new, modern and general-purpose implementation of Taylor’s integration method for the numerical solution of ordinary differential equations. Detailed numerical tests focused on difficult high-precision gravitational problems in astrodynamics and celestial mechanics show how our general-purpose integrator is competitive with and often superior to state-of-the-art specialized symplectic and non-symplectic integrators in both speed and accuracy. In particular, we show how Taylor methods are capable of satisfying Brouwer’s law for the conservation of energy in long-term integrations of planetary systems over billions of dynamical time-scales. We also show how close encounters are modelled accurately during simulations of the formation of the Kirkwood gaps and of Apophis’ 2029 close encounter with the Earth (where heyoka surpasses the speed and accuracy of domain-specific methods). heyoka can be used from both C++ and python, and it is publicly available as an open-source project.
ISSN:0035-8711
1365-2966
DOI:10.1093/mnras/stab1032