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6th and 8th Order Hermite Integrator Using Snap and Crackle

Published online by Cambridge University Press:  01 September 2007

Keigo Nitadori ,
Masaki Iwasawa  and
Junichiro Makino
Keigo Nitadori
Affiliation:
Department of Astronomy, Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan email: nitadori@cfca.jp
Masaki Iwasawa
Affiliation:
Department of General System Studies, Graduate School of Arts and Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8902 email: iwasawa@cfca.jp
Junichiro Makino
Affiliation:
National Astronomical Observatory of Japan, Mitaka, Tokyo, 181-8588, Japan email: makino@cfca.jp
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Abstract

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We present sixth- and eighth-order Hermite integrators for astrophysical N-body simulations, which use the derivatives of accelerations up to second order (snap) and third order (crackle). These schemes do not require previous values for the corrector, and require only one previous value to construct the predictor. Thus, they are fairly easy to be implemented. The additional cost of the calculation of the higher order derivatives is not very high. Even for the eighth-order scheme, the number of floating-point operations for force calculation is only about two times larger than that for traditional fourth-order Hermite scheme. The sixth order scheme is better than the traditional fourth order scheme for most cases. When the required accuracy is very high, the eighth-order one is the best.

Keywords

stellar dynamicsmethods: n-body simulationsmethods: numerical
Type
Contributed Papers
Information
Proceedings of the International Astronomical Union , Volume 3 , Symposium S246: Dynamical Evolution of Dense Stellar Systems , September 2007 , pp. 473 - 474
Copyright
Copyright © International Astronomical Union 2008

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