Journal article
Building a better leapfrog
The Astrophysical journal, v 443(2), pp L93-L96
20 Apr 1995
Abstract
In stellar dynamical computer simulations, as well as other types of simulations using particles, time step size is often held constant in order to guarantee a high degree of energy conservation. In many applications, allowing the time step size to change in time can offer a great saving in computational cost, but variable-size time steps usually imply a substantial degradation in energy conservation. We present a meta-algorithm' for choosing time steps in such a way as to guarantee time symmetry in any integration scheme, thus allowing vastly improved energy conservation for orbital calculations with variable time steps. We apply the algorithm to the familiar leapfrog scheme, and generalize to higher order integration schemes, showing how the stability properties of the fixed-step leapfrog scheme can be extended to higher order, variable-step integrators such as the Hermite method. We illustrate the remarkable properties of these time-symmetric integrators for the case of a highly eccentric elliptical Kepler orbit and discuss applications to more complex problems.
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Details
- Title
- Building a better leapfrog
- Creators
- Piet Hut - Institute for Advanced Study, Princeton, NJJun Makino - University of TokyoSteve Mcmillan - Drexel University
- Publication Details
- The Astrophysical journal, v 443(2), pp L93-L96
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Physics
- Web of Science ID
- WOS:A1995QU58500011
- Scopus ID
- 2-s2.0-11944261676
- Other Identifier
- 991019174910204721
InCites Highlights
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- Collaboration types
- Domestic collaboration
- International collaboration
- Web of Science research areas
- Astronomy & Astrophysics