### Abstract

Several integration schemes exist to solve the equations of motion of the N-body problem. The Lie-integration method is based on the idea to solve ordinary differential equations with Lie-series. In the 1980s, this method was applied to solve the equations of motion of the N-body problem by giving the recurrence formulae for the calculation of the Lie-terms. The aim of this work is to present the recurrence formulae for the linearized equations of motion of N-body systems. We prove a lemma which greatly simplifies the derivation of the recurrence formulae for the linearized equations if the recurrence formulae for the equations of motions are known. The Lie-integrator is compared with other well-known methods. The optimal step-size and order of the Lie-integrator are calculated. It is shown that a fine-tuned Lie-integrator can be 30-40 per cent faster than other integration methods.

Original language | English |
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Pages (from-to) | 1515-1526 |

Number of pages | 12 |

Journal | Monthly Notices of the Royal Astronomical Society |

Volume | 381 |

Issue number | 4 |

DOIs | |

Publication status | Published - Nov 1 2007 |

### Keywords

- Celestial mechanics
- Methods: N-body simulations
- Methods: numerical

### ASJC Scopus subject areas

- Astronomy and Astrophysics
- Space and Planetary Science