Choice of order and extrapolation method in Aarseth-type N-body algorithms

Details Choice of order and extrapolation method in Aarseth-type N-body algorithms Choice of order and extrapolation method in Aarseth-type N-body algorithms

Feb 1988

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1988apj...325..715p&link_type=abstract

Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 325, Feb. 15, 1988, p. 715-721.

Astronomy and Astrophysics

Astrophysics

10

Astronomical Models, Extrapolation, Many Body Problem, Stellar Motions, Accuracy, Algorithms, Cosmology

Scientific paper

The force-versus-time history of a typical particle in a 50-body King model is taken as input data, and its 'extrapolatability' is measured. Extrapolatability means how far the force can be extrapolated, measured in units of a locally defined rate-of-change time scale, and still be within a specified fractional accuracy of the true values. Greater extrapolatability means larger step size, hence greater efficiency, in an Aarseth-type N-body code. Extrapolatability is found to depend systematically on the order of the extrapolation method, but it goes to a finite limit in the limit of large order. A formula for choosing the optimal (most efficient) order for any desired accuracy is given; higher orders than are presently in use are indicated. Neither rational function extrapolation nor a somewhat vector-regularized polynomial method is found to be systematically better than component-wise polynomial extrapolation, indicating that extrapolatability can be viewed as an intrinsic property of the underlying N-body forces, independent of the extrapolation method.

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