Jovian Problem: Performance of Some High-Order Numerical Integrators

Shafiq Ur Rehman

Department of Mathematics, The University of Auckland, Auckland, New Zealand, 2Department of Mathematics, University of Engineering and Technology, Lahore, Pakistan.

DOI: 10.4236/ajcm.2013.33028                

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.

Keywords

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

Conflicts of Interest

The authors declare no conflicts of interest.

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