A Time-Reversible, Regularized, Switching Integrator for the <i>N</i>-Body Problem

Abstract

This article describes a gravitational N-body integration algorithm conserving linear and angular momentum and time-reversal symmetry. Forces are dynamically partitioned based on interbody separation, so that the long-range forces are evaluated relatively rarely, and close approaches are treated by an efficient regularization technique. The method incorporates an automatic stepsize adjustment based on a Sundman time-transformation. Although the scheme is formally second order, the most intensive computations (the close-approach dynamics) are executed at higher order, thus improving the overall accuracy. Numerical experiments indicate that the method can effectively treat few-body gravitational problems with two-body close approaches, and it compares favorably with other schemes presented in the literature.