THE INVARIANT IMBEDDING NUMERICAL METHOD FOR FREDHOLM INTEGRAL EQUATIONS WITH DEGENERATE KERNELS,

Abstract

The report describes application of invariant imbedding in deriving an initial-value method for solving Fredholm integral equations with degenerate kernels. By regarding the solution at a fixed point as a function of the interval of integration, a differential equation is obtained; this equation, combined with knowledge of the solution for one interval length, makes it possible to determine the solution for other lengths. The principal advantage of the initial-value formulation is its ease of resolution by modern digital and analog computers. Emphasis is on the inhomogeneous problem, although some remarks on the eigenvalue problem are included. A FORTRAN program for solving the initial-value problem is also given, with subroutines written for an Adams-Moulton integration scheme with a Runge-Kutta start. (Author)

Document Details

Document Type
Technical Report
Publication Date
May 01, 1968
Accession Number
AD0669342

Entities

People

  • B. J. Vereeke
  • Harriet H. Kagiwada
  • Robert E. Kalaba

Organizations

  • RAND Corporation

Tags

DTIC Thesaurus Topics

  • Analog Computers
  • Computer Programs
  • Computers
  • Differential Equations
  • Eigenvalues
  • Equations
  • Integral Equations
  • Integrals
  • Intervals
  • Mathematical Analysis
  • Mathematics

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)