A NEW DERIVATION OF THE INTEGRO-DIFFERENTIAL EQUATIONS FOR CHANDRASEKHAR'S X AND Y FUNCTIONS

Abstract

The X and Y functions of Chandrasekhar are of great importance in the theory of multiple scattering in a finite slab. Their properties are best determined analytically through the use of integral equations. From the computational view, though, they are best treated as solutions of a system of integro-differential equations. A derivation is produced from first principles which illuminates the nature of the integro-differential equations and which will aid in computational studies of transport processes. A knowledge of integral equations and Chandrasekhar's book, Radiative Transfer, is assumed.

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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1964
Accession Number
AD0610061

Entities

People

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

Organizations

  • RAND Corporation

Tags

Communities of Interest

  • Air Platforms
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Differential Equations
  • Diffuse Reflection
  • Diffusion
  • Equations
  • Geometry
  • Hard Copy
  • Integral Equations
  • Integrals
  • Intensity
  • Inverse Problems
  • Light Scattering
  • Radiation
  • Radiative Transfer
  • Scattering

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Military History of the United States in the 20th Century.