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W. H. Enright, D. J. Higham, B. Owren and P. W. Sharp, “A Survey of the Explicit Runge-Kutta Method,” Technical Report, 291/94, Department of Computer Science, University of Toronto, Toronto, 1994.

has been cited by the following article:

• TITLE: Jovian Problem: Performance of Some High-Order Numerical Integrators

  AUTHORS: Shafiq Ur Rehman

  KEYWORDS: N-Body Simulations; Jovian Problem; Numerical Integrators; CPU-Time

  JOURNAL NAME: American Journal of Computational Mathematics, Vol.3 No.3, August 14, 2013

  ABSTRACT: 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.