PROOF OF THE BASIC INVARIANT IMBEDDING METHOD FOR FREDHOLM INTEGRAL EQUATIONS WITH DISPLACEMENT KERNELS. I,

Abstract

The report discusses a validation for the invariant imbedding method for the case of a Fredholm integral equation in which the forcing term is an exponential function. Application of the invariant imbedding approach has resulted in various transformations for converting integral equations, two-point boundary-value problems, and variational problems into easily computed Cauchy problems. To consolidate these analytic and computational gains and improve understanding of the associated Cauchy problems, this memorandum proves, conversely, that the solution of the Cauchy problem satisfies the original functional equation. AD-690 126, a companion study, completes the validation by offering a proof for the case of a general forcing term g. (Author)

Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1969
Accession Number
AD0690125

Entities

People

  • J. Casti
  • Robert E. Kalaba

Organizations

  • RAND Corporation

Tags

DTIC Thesaurus Topics

  • Boundaries
  • Boundary Value Problems
  • Cauchy Problem
  • Differential Equations
  • Displacement
  • Equations
  • Exponential Functions
  • Integral Equations
  • Integrals
  • Mathematical Analysis
  • Validation

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Software Engineering.