ASYMPTOTIC SERIES FOR THE SOLUTIONS OF LINEAR DIFFERENTIAL-DIFFERENCE EQUATIONS,

Abstract

The problem of determining the asymptotic nature of the solution of linear differential-difference equations of the form x'(t) = A(t)x(t) + B(t)x(t-1), where the coefficients A(t) and B(t) possess asymptotic series expansions has previously been treated only under quite special conditions and by quite complicated methods. The purpose of this paper is to present a new technique which will yield more comprehensive results. To illustrate the method, unhindered by analytic details, the author considers the scalar version of the foregoing equation and treat only the asymptotic series of the solution associated with the characteristic root of the largest real part.

Document Details

Document Type
Technical Report
Publication Date
May 02, 1958
Accession Number
AD0606852

Entities

People

  • Richard E. Bellman

Organizations

  • RAND Corporation

Tags

DTIC Thesaurus Topics

  • Asymptotic Series
  • Coefficients
  • Difference Equations
  • Differential Equations
  • Equations
  • Mathematical Analysis
  • Mathematics
  • Real Variables
  • Sequences

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis