Astronomy and Astrophysics – Astrophysics
Scientific paper
2006-11-14
Astrophys.J.663:1420-1433,2007
Astronomy and Astrophysics
Astrophysics
31 pages, 8 figures. v2: Revised individual-timestepping description, expanded comparison with other methods, corrected error
Scientific paper
10.1086/518641
This paper describes a fourth-order integration algorithm for the gravitational N-body problem based on discrete Lagrangian mechanics. When used with shared timesteps, the algorithm is momentum conserving and symplectic. We generalize the algorithm to handle individual time steps; this introduces fifth-order errors in angular momentum conservation and symplecticity. We show that using adaptive block power of two timesteps does not increase the error in symplecticity. In contrast to other high-order, symplectic, individual timestep, momentum-preserving algorithms, the algorithm takes only forward timesteps. We compare a code integrating an N-body system using the algorithm with a direct-summation force calculation to standard stellar cluster simulation codes. We find that our algorithm has about 1.5 orders of magnitude better symplecticity and momentum conservation errors than standard algorithms for equivalent numbers of force evaluations and equivalent energy conservation errors.
Bertschinger Edmund
Farr Will M.
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