PIRSA:18110058 Scientific Series Other

DOI10.48660/18110058

Series: Colloquium

Portegies Zwart, S. (2018). Reproducibility despite exponential divergence in the Newtonian few-body problem. Perimeter Institute. https://pirsa.org/18110058

Portegies Zwart, Simon. Reproducibility despite exponential divergence in the Newtonian few-body problem. Perimeter Institute, Nov. 14, 2018, https://pirsa.org/18110058 

@misc{ pirsa_PIRSA:18110058,
  doi = {10.48660/18110058},
  url = {https://pirsa.org/18110058},
  author = {Portegies Zwart, Simon},
  keywords = {Other},
  language = {en},
  title = {Reproducibility despite exponential divergence in the Newtonian few-body problem},
  publisher = {Perimeter Institute},
  year = {2018},
  month = {nov},
  note = {PIRSA:18110058 see, \url{https://pirsa.org}}
}

Abstract

Energy and momentum are conserved in Newton's laws of gravitation.
Numerical integration of the equations of motion should comply to
these requirements in order to guarantee the correctness of a
solution, but this turns out to be insufficient.  The steady growth of
numerical errors and the exponential divergence, renders numerical
solutions over more than a dynamical time-scale meaningless.  Even
time reversibility is not a guarantee for finding the definitive
solution to the numerical few-body problem.  As a consequence,
numerical N-body simulations produce questionable results.  Using
brute force integrations to arbitrary numerical precision I will
demonstrate empirically that the statistics of an ensemble of resonant
3-body interactions is independent of the precision of the numerical
integration, and conclude that, although individual solutions using
common integration methods are unreliable, an ensemble of approximate
3-body solutions accurately represent the ensemble of true solutions.

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