The error growth of some symplectic explicit Runge-Kutta Nystrom methods on long N-body simulations

P. W. Sharp, R. Vaillancourt


At one extreme, the global error for symplectic explicit Runge-Kutta Nystrom (SERKN) methods
consists entirely of truncation error and grows as t. At the other extreme, the
global error consists entirely of random round-off error and
grows stochastically as t^1.5. We use numerical testing to investigate how
the global error grows for stepsizes between these two extremes. The testing is
of representative SERKN methods of orders four to seven on three long N-body
simulations of the Solar System. The work also provides an opportunity
to introduce two new test problems for symplectic methods and to present
comparisons of the efficiency of SERKN methods.

Solar System, N-body, long simulations, explicit Nystrom, symplectic, error growth, comparisons

Math Review Classification
Primary 65L05 ; Secondary 70F10

Last Updated
August 24, 2001

17 pages

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