Accession Number : AD0614636

Title :   NUMERICAL RESULTS FOR THE AUXILIARY EQUATION OF RADIATIVE TRANSFER,

Corporate Author : RAND CORP SANTA MONICA CALIF

Personal Author(s) : Bellman,R. ; Kagiwada,H. ; Kalaba,R.

Report Date : APR 1965

Pagination or Media Count : 26

Abstract : A basic problem in astrophysics, meteorology and neutron transport theory is the determination of the internal intensity produced when uniform parallel rays illuminate a slab of finite thickness which both absorbs and scatters radiation isotropically. One approach to this problem is through the intermediate step of determining the source function which represents the rate of production of scattered radiation per unit volume per unit solid angle as a function of the depth below the top surface. Ordinarily this function is characterized as the solution of a singular integral equation, which presents difficulties from the numerical viewpoint. In earlier memoranda the authors derived other differential integral equations for the source function viewed as a function of the thickness of the slab. In this memorandum they present the results of extensive calculations of source functions in both graphical and tabular form. (Author)

Descriptors :   (*INTEGRAL EQUATIONS, NUMERICAL ANALYSIS), (*FUNCTIONS(MATHEMATICS), GRAPHICS), (*TRANSPORT PROPERTIES, INTEGRAL EQUATIONS), TABLES(DATA), OPTICAL PROPERTIES, NEUTRON TRANSPORT THEORY

Distribution Statement : APPROVED FOR PUBLIC RELEASE