Numerical simulation is a standard tool in the repertoire of the modern
physical scientist's study of complex systems.
The astronomical literature is brimming with results of large *N*-body
simulations.
The proliferation of titles such as
``Simulations of Sinking Galaxies'' [33],
``Dissipationless Collapse of Galaxies and Initial Conditions'' [23],
``A Numerical Study of the Stability of Spherical Galaxies'' [24],
``The Global Stability of Our Galaxy'' [30], and
``Dynamical Instabilities in Spherical Stellar Systems'' [4]
shows that much trust is placed in the results of these simulations.

Can these simulation results really be trusted? What conditions must a simulation meet for its accuracy to be assured? Is there a limit on the length of simulated time a system can be followed accurately? What measures can be used to ascertain the accuracy of a simulation? More fundamentally, what do we mean by ``accuracy'' and ``error'' in these simulations?

All these questions have been addressed in the past with varying
degrees of success.
There is still some controversy about whether simulations of *N*-body
systems can be trusted.
The main reason for this concern is that *N*-body systems are *chaotic*
-- small perturbations in the phase-space co-ordinates at any point result in
a vastly different phase-space solution a short time later.
Given that numerical computations are constantly introducing small errors
to the computed solution, we must naturally ask what effect these errors
have on computed solutions.

Sun Dec 29 23:43:59 EST 1996

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