Long initial value test problems from simulations of the Solar System

Abstract

N-body simulations of the Solar System are a rich source of initial value problems for ordinary differential equations. The problems range from the simulation of two bodies requiring a few milliseconds of CPU time to large simulations of a hundred thousand bodies or more requiring CPU time counted in months. We describe five N-body models and use them with long intervals of integration to compare the integrators DIVA, STEP, RKNINT and RKSUITE.