%0 Generic %1 hernandez2019longterm %A Hernandez, David M. %A Hadden, Sam %A Makino, Junichiro %D 2019 %K tifr %T Are long-term $N$-body simulations reliable? %U http://arxiv.org/abs/1910.08667 %X $N$-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.

@misc{hernandez2019longterm, abstract = {$N$-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.}, added-at = {2019-10-22T07:58:40.000+0200}, author = {Hernandez, David M. and Hadden, Sam and Makino, Junichiro}, biburl = {https://www.bibsonomy.org/bibtex/2504ea1efc38b95ba35b9aca4898cff3e/citekhatri}, description = {Are long-term $N$-body simulations reliable?}, interhash = {c3587ceb662ef48523ab966b2447e541}, intrahash = {504ea1efc38b95ba35b9aca4898cff3e}, keywords = {tifr}, note = {cite arxiv:1910.08667Comment: 13 pages, 12 figures, to be submitted to MNRAS, comments welcome}, timestamp = {2019-10-22T07:58:40.000+0200}, title = {Are long-term $N$-body simulations reliable?}, url = {http://arxiv.org/abs/1910.08667}, year = 2019 }