INVARIANT IMBEDDING AND FREDHOLM INTEGRAL EQUATIONS WITH PINCHERLE-GOURSAT KERNELS,

Abstract

An analytical procedure for solving Fredholm integral equations of the second kind with Pincherle-Goursat (degenerate) kernels is discussed. In the invariant imbedding approach used, the solution at a fixed value of t is studied as the length of the interval is varied. A Cauchy problem is derived, and it is verified that the initial-value method produces a solution of the integral equation. Such a procedure should prove a valuable alternative to the usual algebraic method, and should find application in signal detection, gas dynamics, radiative transfer, and mathematical biology. (Author)

Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1968
Accession Number
AD0668759

Entities

People

  • Harriet H. Kagiwada
  • Robert E. Kalaba
  • S. Ueno

Organizations

  • RAND Corporation

Tags

DTIC Thesaurus Topics

  • Cauchy Problem
  • Detection
  • Dynamics
  • Equations
  • Gas Dynamics
  • Integral Equations
  • Integrals
  • Intervals
  • Mathematical Analysis
  • Mathematics
  • Radiative Transfer
  • Signal Detection

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis