``Prediction can be difficult, particularly about the future.''

-- Mark Twain

*
Astrophysical N-body systems are chaotic. In other words, they have
sensitive dependence on initial conditions. This means that the
phase-space distance between two solutions whose initial conditions
differ by an arbitrarily small amount will increase exponentially with
time. Since computers constantly make small errors in the computation
of such solutions, it is guaranteed (with probability 1) that a
computed solution will diverge exponentially from the true solution
with the same initial conditions. Thus, it is possible that
numerical solutions for chaotic systems are overwhelmed by
exponential magnification of small errors, which might mean
computed solutions are worthless. This could be the case even if
quantities such as energy or momentum are conserved to arbitrary
accuracy, because there are infinitely many solutions whose
energy is exactly the same, but have vastly different phase
space trajectories.
*

- Introduction
- History of exponential divergence in
*N*-body systems - The kinds of errors made in
*N*-body simulations - Summary of this thesis

Sun Dec 29 23:43:59 EST 1996

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