ON THE COMPUTATIONAL SOLUTION OF A CLASS OF FUNCTIONAL DIFFERENTIAL EQUATIONS

Abstract

Functional differential equations of the form (1) u'(t) = g(t,u(t), u(h(t))), and, more generally, of the form (2) u'(t) = g(t,u(t), u(h(u,t))), arise in the construction of realistic models in a number of fields, ranging from electromagnetic theory and control theory to respiratory theory and neurophysiology. The analytic aspects are quite complex, and numerical solution is anything but routine, even with the aid of a digital computer. In this paper, a method for the computational treatment of differential-difference equations was extended to cover equations of the form given in (1). Equations of the type appearing in (2) can then be treated by means of successive approximations.

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Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1964
Accession Number
AD0606987

Entities

People

  • K. L. Cooke
  • Richard E. Bellman

Organizations

  • RAND Corporation

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Air Force
  • Complex Systems
  • Control Theory
  • Difference Equations
  • Differential Equations
  • Digital Computers
  • Electromagnetism
  • Engineering
  • Equations
  • Hard Copy
  • Intervals
  • Mathematical Models
  • Mathematics
  • Models
  • Monotone Functions
  • Simultaneous Equations
  • United States

Fields of Study

  • Mathematics

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  • Calculus or Mathematical Analysis
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