A time-symmetric block time-step algorithm for N-body simulations |
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| Affiliation: | 1. Department of Astronomy, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan;2. Institute for Advanced Study, Princeton, NJ 08540, USA;3. Istanbul Technical University, Informatics Institute, Computational Science and Engineering Program, 34469 Maslak, Istanbul, Turkey;4. Istanbul Technical University, Institute of Energy, 34469 Maslak, Istanbul, Turkey;1. School of Physics, Korea Institute for Advanced Study, 85 Hoegi-ro, Dongdaemun-gu, Seoul 130-722, Republic of Korea;2. Center for Advanced Computation, Korea Institute for Advanced Study, 85 Hoegi-ro, Dongdaemun-gu, Seoul 130-722, Republic of Korea;1. The Graduate School of China Academy of Engineering Physics, P.O. Box 2101, Beijing, 100088, China;2. Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing, China;3. Center for Applied Physics and Technology, Peking University, Beijing, China |
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| Abstract: | The method of choice for integrating the equations of motion of the general N-body problem has been to use an individual time step scheme. For the sake of efficiency, block time steps have been the most popular, where all time step sizes are smaller than a maximum time step size by an integer power of two. We present the first successful attempt to construct a time-symmetric integration scheme, based on block time steps. We demonstrate how our scheme shows a vastly better long-time behavior of energy errors, in the form of a random walk rather than a linear drift. Increasing the number of particles makes the improvement even more pronounced. |
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