# Accession Number:

## AD0441212

# Title:

## APPROXIMATE SOLUTION IN A FINITE TIME INTERVAL FOR ORDINARY NONLINEAR DIFFERENTIAL EQUATIONS,

# Descriptive Note:

# Corporate Author:

## STANFORD UNIV CA STANFORD ELECTRONICS LABS

# Personal Author(s):

# Report Date:

## 1962-07-01

# Pagination or Media Count:

## 88.0

# Abstract:

The object of this investigation is to obtain approximate solutions over finite time intervals to ordinary, nonlinear, differential equations. A new method of approximation is introduced which, for a given differential equation and associated initial conditions, yields an approximate solution which is close to the exact solution everywhere in the prescribed time interval. Because of the nature of the approximate solution, an estimate of the solution error can be obtained from the original differential equation. This approximation technique is compared with some well-known method of approximation. Examples are considered in which the approximation method developed in this research gives superior numerical results. Further, problem areas are indicated multiple-degree-of-freedom systems, timevariable systems which are not suitable for treatment by some of the well-known methods but capable of analysis by the technique to be presented in this study. Author