A MULTIRATE STÖRMER ALGORITHM FOR CLOSE ENCOUNTERS

We present, analyze, and test a multirate Störmer-based algorithm for integrating close encounters when performing N-body simulations of the Sun, planets, and a large number of test particles. The algorithm is intended primarily for accurate simulations of the outer solar system. The algorithm uses stepsizes H and hi , i = 1, ..., Np , where hi << H and Np is the number of planets. The stepsize H is used for the integration of the orbital motion of the Sun and planets at all times. H is also used as the stepsize for the integration of the orbital motion of test particles when they are not undergoing a close encounter. The stepsize hi is used to integrate the orbital motion of test particles during a close encounter with the ith planet. The position of the Sun and planets during a close encounter is calculated using Hermite interpolation. We tested the algorithm on two contrasting problems, and compared its performance with the existing method which uses the same stepsize for all bodies (this stepsize must be significantly smaller than H to ensure the close encounters are integrated accurately). Our tests show that the integration error for the new and existing methods are comparable when the stepsizes are chosen to minimize the error, and that for this choice of stepsizes the new method requires considerably less CPU time than the existing method.