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'' , ``Dissipationless Collapse of Galaxies and Initial Conditions'' , ``A Numerical Study of the Stability of Spherical Galaxies'' , ``The Global Stability of Our Galaxy'' , and ``Dynamical Instabilities in Spherical Stellar Systems''  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.