On a time-symmetric Hermite integrator for planetary N-body simulation

Details On a time-symmetric Hermite integrator for planetary N-body simulation On a time-symmetric Hermite integrator for planetary N-body simulation

Jul 1998

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998mnras.297.1067k&link_type=abstract

Monthly Notices of the Royal Astronomical Society, Volume 297, Issue 4, pp. 1067-1072.

Astronomy and Astrophysics

Astronomy

45

Methods: Numerical, Celestial Mechanics, Stellar Dynamics, Solar System: Formation

Scientific paper

We describe a P(EC)^n Hermite scheme for planetary N-body simulation. The fourth-order implicit Hermite scheme is a time-symmetric integrator that has no secular energy error for the integration of periodic orbits with time-symmetric time-steps. In general N-body problems, however, this advantage is of little practical significance, since it is difficult to achieve time-symmetry with individual variable time-steps. However, we can easily enjoy the benefit of the time-symmetric Hermite integrator in planetary N-body systems, where all bodies spend most of the time on nearly circular orbits. These orbits are integrated with almost constant time-steps even if we adopt the individual time-step scheme. The P(EC)^n Hermite scheme and almost constant time-steps reduce the integration error greatly. For example, the energy error of the P(EC)^2 Hermite scheme is two orders of magnitude smaller than that of the standard PEC Hermite scheme in the case of an N=100,m=10^25g planetesimal system with the rms eccentricity ^1/2<~0.03.

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