ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF DIFFERENTIAL-DIFFERENCE EQUATIONS

Abstract

In this paper, the problem was considered of determining the asymptotic behavior of solutions of linear differentialdifference equations whose coefficients possess asymptotic series. Although the problem is considerably more complicated than the corresponding problem for ordinary differential equations, by means of a sequence of transformations the problem was reduced to a form where the standard techniques of ordinary differential equation theory could be employed. The differential-difference equation was transformed into an integral equation which was trans formed into an integro- differential equation. At this point the Liouville transformation plays a vital role. Although the guiding ideas were simple, the analysis became formidable. For this reason, only some of the more immediate aspects of the problem were considered.

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Document Details

Document Type
Technical Report
Publication Date
Aug 28, 1958
Accession Number
AD0607016

Entities

People

  • Kenneth L. Cooke
  • Richard E. Bellman

Organizations

  • RAND Corporation

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Asymptotic Series
  • Coefficients
  • Difference Equations
  • Differential Equations
  • Equations
  • Hypotheses
  • Inequalities
  • Integral Equations
  • Integrals
  • Intervals
  • Kernel Functions
  • Power Series
  • Real Variables
  • Sequences
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)