A New Time-Symmetric Block Time-Step Algorithm for N-Body Simulations
  Time-symmetric integration schemes share with symplectic schemes the property that their energy errors show a much better behavior than is the case for generic integration schemes. Allowing adaptive time steps typically leads to a loss of symplecticity. In contrast, time symmetry can be easily maintained, at least for a continuous choice of time step size. In large-scale N-body simulations, however, one often uses block time steps, where all time steps are forced to take on values as powers of two. This greatly facilitates parallelization, and hence code efficiency. Straightforward implementation of time-symmetry, translated to block time steps, faces significant hurdles. For example, iteration can lead to oscillatory behavior, and even when such behavior is suppressed, energy errors show a linear drift in time. We present an approach that circumvents these problems. 
Murat Kaplan (1), Hasan Saygin (1), Piet Hut (2), Jun Makino (3) (1.   Istanbul Technical University, 2.IAS Princeton, 3.Uni...