Partitioned Linear Multistep Method for Long Term Integration of the N-Body Problem

In this paper an exponential fitted partitioned linear multistep method is developed for the long term integration of the N-body problem. The new method integrates exactly any linear combination of the functions 1, x, x², x³ ,…, x^2k–1, exp(±wx) for the coordinates and any linear combination of the functions 1, x, x², x³,…, x^2k–3, exp(±wx) for the velocities. Numerical results are produced and compared with a set of well known symplectic and single step methods. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)