**DDA 33rd Meeting, Mt. Hood, OR, April 2002**

*Session 8. N-Body Techniques*

Tuesday, April 23, 2002, 8:30-10:20am
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## [8.03] A New Direction for N-body Integrators

*J. Chambers (NASA Ames Research Center)*

Symplectic integrators are widely used for addressing
problems in celestial mechanics. To date, the most popular
algorithms are the 2nd-order (leapfrog) and 4th-order
methods, which require one and three force evaluations per
timestep respectively. Of these, the 4th-order integrator
generally gives better performance for a given amount of
computational effort, but its performance is limited by the
fact that some of its substeps have negative coefficients,
i.e. they go backwards compared to the direction of the main
integration. This implies that the other (positive)
coefficients must be large to compensate. Here I describe a
new approach to designing symplectic integrators that
appears to have been overlooked to date. This approach makes
it possible to design a 4th-order integrator with
coefficients that all have magnitudes less than unity,
substantially reducing the size of the leading error term
compared to the conventional algorithm. I will also describe
a new 3rd-order integrator with very small error terms which
has no analogue among conventional symplectic algorithms.
The performance of the new algorithms will be compared with
the standard 2nd and 4th-order methods for several test
problems.

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Bulletin of the American Astronomical Society, **34**, #3

© 2002. The American Astronomical Society.