Parametric Techniques for Eliminating Division and Treating Singularities in Computer Solutions of Ordinary Differential Equations

Abstract

By using the analog-computer independent variable time, as a parameter, a differential equation can be transformed into a set of first-order equations containing no divisions. This makes it possible, by means of other mathematical transformations to prevent unbounded functions from occurring during a computation and sometimes to continue solutions through singularities. The discussion includes a detailed application of the method to a second-order differential equation containing both zero and infinite slopes in the solution. The graph of the solution is obtained without reprogramming and with less equipment than that required by usual techniques.