Forward Symplectic Integrators for Solving Gravitational Few-Body Problems

Details Forward Symplectic Integrators for Solving Gravitational Few-Body Problems Forward Symplectic Integrators for Solving Gravitational Few-Body Problems

2003-04-11

arxiv.org/abs/astro-ph/0304223v1

Astronomy and Astrophysics

Astrophysics

21 pages, 10 figures, use aastex; submitted to The Astronomical Journal

Scientific paper

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.

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