A note concerning Gauss-Jackson method

Specialized literature concerning studies on Orbital Dynamics usually mentions the Gauss-Jackson or sum squared (?2) method for the numerical integration of second order differential equations. However, as far as we know, no detailed description of this code is available and there is some confusion about the order of the method and its relation with the Störmer method. In this paper we present a simple way of deriving this algorithm and its corresponding analog for first order equations from the Störmer and Adams methods respectively. We show that the Gauss-Jackson method can be conceived as a consequence of this, and therefore there is no difficulty in determining the order of the method. Finally, we obtain an initialization technique for its implementation, we show an advantage of it as compared with the traditional multistep methods when applied in PEC mode by supressing the corrector stage in the intermediate steps