The following book discusses the Gauss-Jackson predictor-corrector:

"Astrodynamics Orbit Determination, Space Navigation, Celestial Mechanics" by Samuel Herrick, Van Nost4and Reinhold Company, 1971,

The book is in two volumes. The second volume discusses Gauss-Jackson.

Herrick is very thorough but uses a notation that can be difficult to read. His book might(?) be out of print.

A more readable book that's very easy to find is:

"Fundamentals of Astrodynamics" by Bate, Mueller and White. Dover Publications, Inc., 1971. isbn 0-486-60061-0.

I suggest getting your feet wet with "Fundamentals of Astrodynamics". If you want to learn more then go on to Herrick.

A lot of technical talent was spent on the Gauss-Jackson algorthim. During the Cold War, it was the main method used by the United States Air Force for calculating spacecraft and ICBM trajectories. They poured buckets of money on it. The favorite Gauss-Jackson version used by the USAF/Space Division was the 8th order predictor-corrector with a variable step size control algorithm.

Gary