Multistep Methods for the Numerical Solution of Ordinary Differential Equations Made Self-Starting

摘要

Milne's method and other similar multistep ones for the approximate solution of differential equations, are not selfstarting. They require the use of known p pivotal points (x sub i, y(x sub i)), i = 0,1, ... , (p-1), where x's are equally spaced and y = y(x) is the solution of the differential equation. Usually these pivotal points are generated through the use of a set of so-called p-point formulas, preferably p being an odd integer. But these p-point formulas are not self-starting either. A rational method is established herein which will make these p-point formulas, and consequently also the multistep methods, self-starting. Subsequently the method is extended to systems of differential equations. (Author)