2003/04/11 by Siu A. Chin, Chin, Siu A., C. R. Chen +1 · 1 citation
Physics and Astronomy · #Astrophysics (astro-ph) #Computational Physics (physics.comp-ph) #FOS: Physical sciences #astro-ph #physics.comp-ph
paper · pdf · doi:10.48550/arxiv.astro-ph/0304223
21 pages, 10 figures, use aastex; submitted to The Astronomical Journal
arxiv created 2003/04/11 · arxiv updated 2009/12/01
We introduce a class of fourth order symplectic algorithms that are ideal for doing long time integration of gravitational few-body problems. These algorithms have only positive time steps, but require computing the force gradient in additional to the force. We demonstrate the efficiency of these Forward Symplectic Integrators by solving the circularly restricted three-body problem in the space-fixed frame where the force on the third body is explicitly time-dependent. These algorithms can achieve accuracy of Runge-Kutta, backward time step and corrector symplectic algorithms at step sizes five to ten times as large.