JANUS: A bit-wise reversible integrator for N-body dynamics

Abstract

Hamiltonian systems such as the gravitational N-body problem have time-reversal symmetry. However, all numerical N-body integration schemes, including symplectic ones, respect this property only approximately. In this paper, we present the new N-body integrator JANUS, for which we achieve exact time-reversal symmetry by combining integer and floating point arithmetic. JANUS is explicit, formally symplectic and satisfies Liouville's theorem exactly. Its order is even and can be adjusted between two and ten. We discuss the implementation ofJANUS and present tests of its accuracy and speed by performing and analyzing long-term integrations of the Solar System. We show that JANUS is fast and accurate enough to tackle a broad class of dynamical problems. We also discuss the practical and philosophical implications of running exactly time-reversible simulations.

Accepted for publication by MNRAS, 7 pages, 4 figures, source code available at https://github.com/hannorein/rebound , iPython notebooks to reproduce figures available at https://github.com/hannorein/JanusPaper

References in corpus (4)

• WHFast: A fast and unbiased implementation of a symplectic Wisdom-Holman integrator for long term gravitational simulations
• Explicit methods in extended phase space for inseparable Hamiltonian problems
• A new paradigm for reproducing and analyzing N-body simulations of planetary systems
• Fast and reliable symplectic integration for planetary system $N$-body problems

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