THE INVARIANT IMBEDDING NUMERICAL METHOD FOR FREEDHOLM INTEGRAL EQUATIONS WITH DISPLACEMENT KERNELS,

Abstract

A computer program for the solution of a Fredholm integral equation of the second kind with a displacement kernel is given. The Fredholm integral equation is transformed into an initial-value problem by treating the interval length as the independent variable. The method of reduction is invariant imbedding. The numerical integration is accomplished by using a fourth-order Adams-Moulton predictor-corrector method, with a fourth-order Runge-Kutta method to start the process. The program was used to solve the basic integral equation of radiative transfer, and results were compared with those obtained by Sobolev, by Viskanta, by Bellman, Kagiwada, and Kalaba, and by Heaslet and Warming. Results were in excellent agreement. (Author)

Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1969
Accession Number
AD0685709

Entities

People

  • Harriet H. Kagiwada
  • J. Casti
  • Robert E. Kalaba

Organizations

  • RAND Corporation

Tags

DTIC Thesaurus Topics

  • Agreements
  • Computer Programs
  • Computers
  • Displacement
  • Equations
  • Integral Equations
  • Integrals
  • Intervals
  • Mathematical Analysis
  • Numerical Integration
  • Radiative Transfer
  • Runge Kutta Method

Fields of Study

  • Mathematics

Readers

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