Initial value methods for the basic boundary value problem and integral equation of radiative transfer

by H. H. Natsuyama, Robert E. Kalaba

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A new approach to the study of integral equations and linear unstable two-point boundary-value problems. The Memorandum considers the problem of radiative transfer in a plane-parallel atmosphere which absorbs radiation and scatters it isotropically, there being a continuous distribution of primary internal sources of radiation. An effective numerical technique for calculating the internal intensity and the source functions is sought. A major consideration is the computer's ability to solve initial-value problems for large systems of ordinary differential equations. The authors derive new differential-integral equations for the internal intensity at a fixed point and direction, and the source function at a fixed point, the new independent variable being the thickness of the atmosphere. Using standard quadrature techniques, they approximate these equations by systems of ordinary differential equations whose numerical treatment is straightforward. 20 pp.

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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