Symplectic variable step size integration for N-body problems

Multiple time stepping can be applied to the leapfrog/Stormer/Verlet integr ator so as to effect a variable step size algorithm. The strategy maintains the symplecticness, time-reversibility, and second-order accuracy of the l eapfrog method. This method can be applied to 2-body central force interact ions by partitioning them into distance classes and smoothly decomposing th e potential energy into the sum of potential functions for the respective c lasses. The algorithm described here is much more efficient than leapfrog w ith very small step sizes and more accurate than leapfrog with larger step sizes. (C) 1999 Elsevier Science B.V. and IMACS. All rights reserved.