Errors, chaos and the collisionless limit

Understand

We simultaneously study the dynamics of the growth of errors and the question of the faithfulness of simulations of $N$-body systems.

• The errors are quantified through the numerical reversibility of small-$N$ spherical systems, and by comparing fixed-timestep runs with different stepsizes.
• The errors add randomly, before exponential divergence sets in, with exponentiation rate virtually independent of $N$, but scale saturating as $\sim 1/\sqrt{N}$, in line with theoretical estimates presented.
• In a third phase, the growth rate is initially driven by multiplicative enhancement of errors, as in the exponential stage.