A new initial value method for internal intensities in radiative transfer

Harriett H. Natsuyama, Robert E. Kalaba

ResearchPublished 1966

Presentation of an improved technique for determining internal intensities for transport porcesses in finite slabs where absorption and multiple scattering occur. Traditional approaches involve solving either an unstable linear two-point boundary-value problem or a singular integral equation, both of which have computational drawbacks. This new method, however, has computational and analytical advantages, for it leads to the integration of an initial value problem for a system of ordinary differential equations, a suitable task for digital computers. Some typical results are presented as well as comparisons against other calculations. The authors also show how certain problems involving tow-point boundary conditions or singular integral equations can be converted into stable initial-value problems, a major step in mathematical physics and engineering.

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Natsuyama, Harriett H. and Robert E. Kalaba, A new initial value method for internal intensities in radiative transfer. Santa Monica, CA: RAND Corporation, 1966. https://www.rand.org/pubs/research_memoranda/RM4906.html.
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