An Extension of Milne's Three-Point Method

Abstract

Milne's thr~e-point integration method uses a fixed integration step size, chosen to satisfy convergence and truncation error conditions at the worst possible point in the integration interval. Usually this step size is too small in most sections of the interval. In this paper, Milne's method is extended to it~l allow the use of a variable step size, the step being adiusted according to the conditions in the immediate neighborhood of the integration point. This method has the advantage of using the largest step consistent with convergence and accuracy requirements. In two applications of this method on a high-speed digital computer, it is estimated that the computing time required for Milne's lli method with a fixed step size would have been from 16 to 256 times greater than for the method described here.