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.