APPROXIMATE SOLUTIONS OF A NON-LINEAR DIFFERENTIAL EQUATION USING LAPLACE-TRANSFORM AND REVERSION-OF-SERIES TECHNIQUES.

Abstract

The reversion-of-series method is extended to the s - domain by using non-linear Laplace transforms. The reversion of series in the s - domain is applied to a non-linear differential equation and approximate solutions are obtained. The approximate solution is modified for the case where the steady state is a constant value by calculating the exact steady-state value and applying it to the reversion approximation. The non-linear differential equation considered is Duffing's equation with a damping term and sinusoidal and constant forcing functions. The theoretical solutions are compared to machine solutions. (Author)

Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1969
Accession Number
AD0705490

Entities

People

  • Walter Tarnopilsky

Organizations

  • Naval Postgraduate School

Tags

DTIC Thesaurus Topics

  • Differential Equations
  • Equations
  • Linear Differential Equations
  • Mathematical Analysis
  • Mathematics
  • Steady State

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Structural Dynamics.