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

  • Keigo Nitadori (a1), Masaki Iwasawa (a2) and Junichiro Makino (a3)
Abstract

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.

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Copyright
References
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Aarseth, J. S., 2003, Gravitational N-Body Simulations [Cambridge Univ. Pr.]
Heggie, D. C. & Mathieu, R. D. 1986, The Use of Supercomputers in Stellar Dynamics, 267, 233
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Nitadori, K., Makino, J., & Hut, P. 2006, New Astronomy, 12, 169
Nitadori, K. & Makino, J. 2007, ArXiv e-prints, 708, arXiv:0708.0738
Warren, M. S., Salmon, J. K., Becker, D. J., Goda, M. P., & Sterling, T. 1997, In The SC97 Proceedings, CD–ROM. IEEE, Los Alamitos, CA
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Proceedings of the International Astronomical Union
  • ISSN: 1743-9213
  • EISSN: 1743-9221
  • URL: /core/journals/proceedings-of-the-international-astronomical-union
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