Methods for the Global Solution of Differential Equations,

Abstract

In the paper, the author discusses a novel class of methods for obtaining global approximations to solutions of differential and other functional equations. Most of the techniques which have been devised for obtaining approximate solutions for differential equations are based on the following philosophy: one uses the equation as it stands, and then seeks to satisfy the equation approximately by various means such as power series, Fourier series, expansions in series of other functions or by use of finite difference schemes. Our approach reverses this procedure. The author solves an approximate equation, but solves it exactly. The methods discussed are thus philosophically more akin to the usual techniques for obtaining uniform asymptotic solutions of differential equations in the neighborhood of a turning point by constructing solutions of an equation which is similar to, but simpler than, the original equation. (Author)

Document Details

Document Type
Technical Report
Publication Date
Oct 02, 1972
Accession Number
AD0751280

Entities

People

  • Yudell L. Luke

Organizations

  • University of Missouri–Kansas City

Tags

DTIC Thesaurus Topics

  • Differential Equations
  • Equations
  • Fourier Series
  • Mathematical Analysis
  • Mathematics
  • Philosophy
  • Power Series
  • Sequences
  • Sequences (Mathematics)

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Control Systems Engineering.
  • Operations Research