Switching integrators reversibly in the astrophysical N-body problem

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.