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

TL;DR

This paper introduces a reversible switching algorithm for N-body integrators that improves long-term accuracy in simulating planetary systems with close encounters and eccentric orbits.

Contribution

The authors develop a simple, reversible switching method for N-body integrators that reduces long-term errors without significant computational cost.

Findings

Reversible switching reduces error accumulation in N-body simulations.

A few percent of steps violate symmetry without correction, leading to errors.

The method maintains accuracy over long-term integrations.

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.