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- Reproducibility despite exponential divergence in the Newtonian few-body problem

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.

Collection/Series:

Event Type:

Seminar

Speaker(s):

Event Date:

Wednesday, November 14, 2018 - 14:00 to 15:30

Location:

Time Room

Room #:

294

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