Symplectic fourth-order maps for the collisional N-body problem

We study analytically and experimentally certain symplectic and time-reversible N-body integrators which employ the Kepler solver for each pairwise interaction, including the method of Hernandez & Bertschinger. Owing to the Kepler solver, these methods treat close two-body interactions correctly, while close three-body encounters contribute to the truncation error at second order and above. The second-order errors can be corrected to obtain a fourth-order scheme with little computational overhead. We generalize this map to an integrator which employs the Kepler solver only for selected interactions and yet retains fourth-order accuracy without backward steps. In this case, however, two-body encounters not treated via the Kepler solver contribute to the truncation error.