Switching integrators reversibly in the astrophysical $N$-body problem

Abstract

We present a simple algorithm to switch between $N$-body time integrators in a reversible way. We apply it to planetary systems undergoing arbitrarily close encounters and highly eccentric orbits, but the potential applications are broader. Upgrading an ordinary non-reversible switching integrator to a reversible one is straightforward and introduces no appreciable computational burden in our tests. Our method checks if the integrator during the time step violates a time-symmetric selection condition and redoes the step if necessary. In our experiments a few percent of steps would have violated the condition without our corrections. By eliminating them the algorithm avoids long-term error accumulation, of several orders magnitude in some cases.

10 pages, 8 figures. Matches accepted MNRAS version

References in corpus (12)

• PeTar: a high-performance N-body code for modeling massive collisional stellar systems
• Hybrid Symplectic Integrators for Planetary Dynamics
• N-body simulations of gravitational dynamics
• The fate of planetesimal discs in young open clusters: implications for 1I/'Oumuamua, the Kuiper belt, the Oort cloud and more
• A Time-Symmetric Block Time-Step Algorithm for N-Body Simulations
• Dynamic stability of the Solar System: Statistically inconclusive results from ensemble integrations
• Time-symmetric integration in astrophysics
• Towards time symmetric N-body integration
• Are long-term $N$-body simulations reliable?
• A differentiable N-body code for transit timing and dynamical modeling. I. Algorithm and derivatives
• Stepsize errors in the $N$-body problem: discerning Mercury's true possible long-term orbits
• Should $N$-body integrators be symplectic everywhere in phase space?