Figure 2

Divergence for the equilateral triangle configuration. In the left panel we show the divergence as a function of time. The solid, black curves compare Brutus solutions with increasing precision, where subsequent precisions are increased by 10 orders of magnitude and where the word-length is a function of tolerance as in equation (4). The dotted, green curves show results for similar simulations, but with a much longer, fixed word-length of 512 bits. The initial power law phase of divergence lasts longer in this case. The exponential divergence becomes dominant when the round-off error has had time to accumulate to become of the order the discretisation error. The dashed, red curves compare the highest precision Brutus solution with Hermite solutions with time-step parameters 10⁻¹, 10⁻², 10⁻³ and 10⁻⁴. In the right panel we show for Brutus, the duration for which the triangular configuration remains intact as a function of Bulirsch-Stoer tolerance ϵ. Note that the time is in units of the period of one complete rotation of the system. The small scatter in the data is due to the discrete times at which we check the triangular configuration.