Computable Bounds for Solutions of Integral Equations.

Abstract

Interval integration is used to obtain inclusions of integral operators of the form g(u)(s) = integral of T(g(s,t,u(s),u(t))dt) which can be carried out on a computer. The resulting inclusions, combined with interval iteration, are used to compute guaranteed upper and lower bounds for solutions of integral equations of the form u = g(u) for s is an element of S. It is also possible to establish existence or nonexistence of solutions of integral equations in given regions on the basis of results of the computation. Examples of applications of this technique to linear and nonlinear integral equations are eigenvalue problems for linear integral operators are given. Keywords: Integral equations; Eigenvalue problems; Error bounds; Interval integration, Interval iteration.

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Document Details

Document Type
Technical Report
Publication Date
May 01, 1985
Accession Number
ADA158189

Entities

People

  • Louis B. Rall

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Abstracts
  • Arithmetic
  • Classification
  • Computations
  • Computers
  • Contracts
  • Eigenvalues
  • Equations
  • Floating Point Operations
  • Integral Equations
  • Integral Transforms
  • Integrals
  • Mainframe Computers
  • Mathematics
  • Numerical Analysis
  • Step Functions
  • United States

Fields of Study

  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.
  • Operations Research
  • Wave Propagation and Nonlinear Chaotic Dynamics.