Jovian Problem: Performance of Some High-Order Numerical Integrators

Shafiq Ur Rehman^{*}

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*N*-body simulations of the Sun, the planets,
and small celestial bodies are frequently used to model the evolution of the Solar
System. Large numbers of numerical integrators for performing such simulations
have been developed and used; see, for example, [1,2]. The primary
objective of this paper is to analyse and compare the efficiency and the error
growth for different numerical integrators. Throughout the paper, the
error growth is examined in terms of the global errors in the positions and
velocities, and the relative errors in the energy and angular momentum of the
system. We performed numerical experiments for the different integrators
applied to the Jovian problem over a long interval of duration, as long as one
million years, with the local error tolerance ranging from 10^{-16 }to 10^{-18}.

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