AN ITERATIVE PROCEDURE FOR THE ANALYSIS OF NONLINEAR NETWORKS.

Abstract

The purpose of this work is to obtain a practical analytical method for the analysis of certain nonlinear networks. To do this, an iterative procedure is developed, and its ability to easily generate good approximate solutions is examined. Association of an auxiliary linear system with the nonlinear system provides the basis of the method, and iterations are carried out by driving the linear system with an error function obtained from the nonlinear system. A proof is given showing that the procedure coverages for a wide variety of auxiliary linear systems. Application of the method is made to a first-order nonlinear equation using several different auxiliary linear equations; it is shown that the choice of linear equation determines the time interval over which the approximation is best. Picard's successive-approximation method is shown to be a special case of the iterative procedure, wherein the auxiliary linear model is a pure integrator; however, if a small-signal linearization is used to select the auxiliary linear model, the procedure is then shown to be very similar to the classical method of perturbations. (Author)

Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1965
Accession Number
AD0474129

Entities

People

  • C. S. Burrus

Organizations

  • Stanford University

Tags

DTIC Thesaurus Topics

  • Equations
  • Integrators
  • Intervals
  • Iterations
  • Linear Systems
  • Mathematical Analysis
  • Mathematics
  • Nonlinear Systems
  • Numerical Analysis
  • Perturbations
  • Time Intervals

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Control Systems Engineering.
  • Systems Analysis and Design