Numerical Experiments on the Efficiency of Second-Order Mixed-Variable Symplectic Integrators for N-Body Problems

Details Numerical Experiments on the Efficiency of Second-Order Mixed-Variable Symplectic Integrators for N-Body Problems Numerical Experiments on the Efficiency of Second-Order Mixed-Variable Symplectic Integrators for N-Body Problems

Dec 1996

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996cemda..65..355m&link_type=abstract

Celestial Mechanics and Dynamical Astronomy, Volume 65, Issue 4, pp.355-371

Astronomy and Astrophysics

Astronomy

12

Numerical Integrations, Symplectic Integrators, Three-Body Problem

Scientific paper

We discuss the efficiency of the so-called mixed-variable symplectic integrators for N-body problems. By performing numerical experiments, we first show that the evolution of the mean error in action-like variables is strongly dependent on the initial configuration of the system. Then we study the effect of changing the stepsize when dealing with problems including close encounters between a particle and a planet. Considering a previous study of the slow encounter between comet P/Oterma and Jupiter, we show that the overall orbital patterns can be reproduced, but this depends on the chosen value of the maximum integration stepsize. Moreover the Jacobi constant in a restricted three-body problem is not conserved anymore when the stepsize is changed frequently: over a 105 year time span, to keep a relative error in this integral of motion of the same order as that given by a Bulirsch-Stoer integrator requires a very small integration stepsize and much more computing time. However, an integration of a sample including 104 particles close to Neptune shows that the distributions of the variation of the elements over one orbital period of the particles obtained by the Bulirsch-Stoer integrator and the symplectic integrator up to a certain integration stepsize are rather similar. Therefore, mixed-variable symplectic integrators are efficient either for N-body problems which do not include close encounters or for statistical investigations on a big sample of particles.

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