Comparisons of high order Stormer and explicit Runge-Kutta Nystrom methods for N-body simulations of the solar system

Abstract

We compare the efficiency, stability properties, overhead, round-off error propagation and storage requirements of fixed-stepsize high order Stormer and explicit Runge-Kutta Nystrom methods for N-body simulations of the solar system. The comparisons of the round-off error propagation and efficiency are made using realistic problems, one of which requires over 500 million integration steps. We find high order ERKN methods have better stability properties and smaller overhead than Stormer methods. Our numerical tests suggest ERKN methods are more efficient than Stormer methods for shorter simulations such as one that simulates ten million years of the jovian planets. However, the superior round-off error propagation of the Stormer method Comment: a) The Math Reviews classification above is for the 2000 MSC system, b) A pdf version of the file is available with the postscript and dvi versions