A Discrete Approximation Framework for Hereditary Systems.

Abstract

A discrete approximation framework for initial-value problems involving certain classes of linear functional differential equations (FDE) of the retarded type is constructed. An equivalence between the FDE and abstract evolution equations (AEE) in an appropriately chosen Hilbert space is established. This equivalence is then employed in the development of discrete approximation schemes in which the infinite-dimensional AEE is replaced by a finite-dimensional system of difference equations. Convergence and rates of convergence are demonstrated via the properties of rational functions with operator arguments and both classical and recent results from linear semigroup theory. Two examples of families of approximation schemes which are included in the general framework and which may be implemented directly on high-speed computing machines are developed. A numerical study of examples which illustrates the application and feasibility of the approximation techniques in a variety of problems together with a summary and analysis of the numerical results are also included. (Author)

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Document Details

Document Type
Technical Report
Publication Date
May 01, 1980
Accession Number
ADA089726

Entities

People

  • I. G. Rosen

Organizations

  • Brown University

Tags

Communities of Interest

  • Air Platforms
  • Autonomy
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Abstracts
  • Air Force
  • Applied Mathematics
  • Banach Space
  • Complex Variables
  • Computational Fluid Dynamics
  • Computational Science
  • Convergence
  • Difference Equations
  • Differential Equations
  • Equations
  • Functional Analysis
  • Hilbert Space
  • Partial Differential Equations
  • Rational Functions
  • Real Variables
  • Theorems

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Calculus or Mathematical Analysis

Technology Areas

  • Space