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Requirements of a Package for N-Body Simulations of the Solar System

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Abstract

N-body simulations of the Solar System form a challenging set of initial value problems for numerical integrators. The challenge comes from the variety of problems and their size – one recent simulation had 300,015 second order equations and required 9×1010 integration steps. A number of packages for specific types of simulations are available. I discuss what is required of a package intended to efficiently perform a wide range of N-body simulations.

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References

  1. M.P. Calvo and J.M. Sanz-Serna, The development of variable-step symplectic integrators, with applications to the two-body problem, SIAM J. Sci. Statist. Comput. 14 (1993) 936–952.

    Google Scholar 

  2. M.P. Calvo and J.M. Sanz-Serna, High-order symplectic Runge-Kutta-Nyström methods, SIAM J. Sci. Comput. 14(5) (1993) 1237–1252.

    Google Scholar 

  3. J.E. Chambers, A hybrid symplectic integrator that permits close encounters between massive bodies, Monthly Notices Royal Astronom. Soc. 304 (1999) 793–799.

    Google Scholar 

  4. J.E. Chambers and M.A. Murison, Pseudo-high-order symplectic integrators, Astron. J. 199 (2000) 425–433.

    Google Scholar 

  5. L-Y. Chou, On order 5 and 6 symplectic explicit Runge-Kutta-Nyström methods, M.Sc. thesis, Department of Mathematics, University of Auckland (2000).

  6. L-Y. Chou and P.W. Sharp, On order 5 symplectic explicit Runge-Kutta-Nyström methods, J. Appl. Math. Decision Sci. 4(2) (2000) 143–150.

    Google Scholar 

  7. J.R. Dormand, M.E.A. El-Mikkawy and P.J. Prince, High-order embedded RKN formulae, IMA J. Numer. Anal. 7 (1987) 423–430.

    Google Scholar 

  8. M. Duncan and H. Levison, SWIFT, http://k2.boulder.swri.edu/?hal/swift.html.

  9. J.M. Fine, Low order practical Runge-Kutta-Nyström methods, Computing 38 (1987) 281–297.

    Google Scholar 

  10. K.R. Grazier, The stability of planetesimal niches in the outer solar system: A numerical study, Ph.D. thesis, University of California, Los Angeles (1997).

    Google Scholar 

  11. K. Grazier, W.I. Newman, W.M. Kaula and J.M. Hyman, Dynamical evolution of planetesimals in the outer solar system: I. The Jupiter/Saturn zone, Icarus 140 (1999) 341–352.

    Google Scholar 

  12. E. Hairer, S.P. N¸rsett and G. Wanner, Solving Ordinary Differential Equations I: Nonstiff Problems, Springer Series in Computational Mathematics, Vol. 8 (Springer, New York, 1987).

    Google Scholar 

  13. T.-Y. Huang and K. Innanen, A survey of multiderivative multistep integrators, Astron. J. 112(1) (1996) 1254–1262.

    Google Scholar 

  14. M.A. López-Marcos, J.M. Sanz-Serna and R.D. Skeel, Explicit symplectic integrators using Hessianvector products, SIAM J. Sci. Comput. 18(1) (1997) 233–238.

    Google Scholar 

  15. R. McLachlan, On the numerical integration of ordinary differential equations by symmetric composition methods, SIAM J. Sci. Comput. 16 (1995) 151–168.

    Google Scholar 

  16. S. Moshier, DE118i, http://people.ne.mediaone.net/moshier/index.html.

  17. X.X. Newhall, E.M. Standish, Jr. and J.G. Williams, DE102: A numerically integrated ephemeris of the Moon and the planets spanning forty-four centuries, Astron. Astrophys. 125 (1983) 150–167.

    Google Scholar 

  18. D. Okunbor and R.D. Skeel, Explicit canonical methods for Hamiltonian systems, Math. Comp. 59 (1992) 439–455.

    Google Scholar 

  19. T. Quinn, N. Katz, J. Stadel and G. Lake, Timing stepping N-body simulations, submitted to Astron. J.

  20. G. Rowlands, A numerical algorithm for Hamiltonian systems, J. Comput. Phys. 97 (1991) 235–239.

    Google Scholar 

  21. P. Saha and S. Tremaine, Long-term planetary integration with individual time steps, Astron. J. 108 (1994) 1962–1969.

    Google Scholar 

  22. L.F. Shampine and M.K. Gordon, Computer Solution of Ordinary Differential Equations; The Initial Value Problem (Freeman, San Francisco, CA, 1975).

    Google Scholar 

  23. P.W. Sharp, Order five explicit second-derivative Runge-Kutta pairs with interpolants, Report Series No. 312, Department of Mathematics, University of Auckland (1994).

  24. P.W. Sharp, Comparisons of high order Stormer and explicit Runge-Kutta methods for N-body simulations of the Solar system, Report Series 449, Department of Mathematics, University of Auckland (2000).

  25. P.W. Sharp and J.M. Fine, Some Nyström pairs for the general second order initial value problem, J. Comput. Appl. Math. 42 (1992) 279–291.

    Google Scholar 

  26. F. Varadi, NBI, http://www.astrobiology.ucla.edu/?varadi/NBI/NBI.html.

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Sharp, P. Requirements of a Package for N-Body Simulations of the Solar System. Numerical Algorithms 31, 271–279 (2002). https://doi.org/10.1023/A:1021151220482

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