Numerical results for the auxiliary equation of radiative transfer

by Richard Ernest Bellman, H. H. Natsuyama, Robert E. Kalaba

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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. The Memorandum presents the results of extensive calculations of source functions in both graphical and tabular form. 29 pp. (See also RM-4531-PR.)

This report is part of the RAND Corporation Research memorandum series. The Research Memorandum was a product of the RAND Corporation from 1948 to 1973 that represented working papers meant to report current results of RAND research to appropriate audiences.

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