Switching integrators reversibly in the astrophysical N-body problem

• Published in: Monthly notices of the Royal Astronomical Society Vol. 522; no. 3; pp. 4639 - 4648
• Main Authors: Hernandez, David M, Dehnen, Walter
• Format: Journal Article
• Language: English
• Published: Oxford University Press 02.05.2023
• Subjects: methods: numerical; planets and satellites: dynamical evolution and stability; celestial mechanics
• ISSN: 0035-8711; 1365-2966
• DOI: 10.1093/mnras/stad657

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 whether the integrator during the time-step violates a time-symmetric selection condition and redoes the step if necessary. In our experiments, a few per cent of steps would have violated the condition without our corrections. By eliminating them, the algorithm avoids long-term error accumulation, of several orders of magnitude in some cases.