Numerical experiments on the efficiency of second-order mixed-variable symplectic integrators for N-body problems View Full Text


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Article Info

DATE

1996-12

AUTHORS

Patrick Michel, Giovanni H. Valsecchi

ABSTRACT

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. More... »

PAGES

355-371

References to SciGraph publications

  • 1988-03. Numerical integration methods in dynamical astronomy in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1980. Introduction to Numerical Analysis in NONE
  • 1984-06. Numerical integration of the equations of motion of celestial mechanics in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1993-03. Recent progress in the theory and application of symplectic integrators in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1990-03. Symplectic integrators and their application to dynamical astronomy in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1991-09. Symplectic integrators for long-term integrations in celestial mechanics in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
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    http://scigraph.springernature.com/pub.10.1007/bf00049500

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    http://dx.doi.org/10.1007/bf00049500

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