REGARDING THE ABSOLUTE STABILITY OF STORMER-COWELL METHODS

摘要

High order variants of the classical St0rmer-Cowell methods are still a popular class of methods for computations in celestial mechanics. In this work we shall investigate the absolute stability of St0rmer-Cowell methods close to zero, and present a characterization of the stability of methods of all orders. In particular, we show that many methods are not absolutely stable at any point in a neighborhood of the origin.