“Stable Predictor-Corrector Methods for Ordinary Differential Equations”, 1959 (; backlinks):
Milne’s method is the classic “predictor-corrector method” for solving ordinary differential equations. In spite of its known instability property, Milne’s method has a number of virtues not possessed by its principal rival, the Runge-Kutta method, which are especially important when the order of the system of equations is fairly high (n = 10–30 or more). Hence it is worth examining predictor-corrector methods that do not have this instability property and at the same time are well adapted to machine computation.
This paper gives a general technique for finding such stable methods, discusses one specific case which seems “on the average” to be a good compromise between conflicting interests, and sketches a second example.