http://arxiv.org/abs/1910.08667
$N$-body integrations are used to model a wide range of astrophysical dynamics, but they suffer from errors which make their orbits diverge exponentially in time from the correct orbits. Over long time-scales, their reliability needs to be established. We address this reliability by running a three-body planetary system over about $200$ e-folding times. Using nearby initial conditions, we can construct statistics of the long-term phase-space structure and compare to rough estimates of resonant widths of the system. Our statistics are approximately consistent for a wide range of numerical methods, including a Runge–Kutta method, Wisdom–Holman method, symplectic corrector methods, and a method by Laskar & Robutel. “Improving” an integrator did not affect the phase space accuracy, but simply increasing the number of initial conditions did.
D. Hernandez, S. Hadden and J. Makino
Tue, 22 Oct 19
11/91
Comments: 13 pages, 12 figures, to be submitted to MNRAS, comments welcome