Abstract
In the present paper, assuming that the radiative transfer in turbed slab bounded below by the imperfect specular reflector is the Markovian process, and starting with the modified Chapman-Kolmogorov equation for a uniform monodirectional illumination, we obtained the Riccati-type of the nonlinear integro-differential equation governing the angular distribution of the radiation emergent from the slab. In other words, without solving the transfer equation, the two-point boundary value problem is reduced to an initial-value problem, by which the numerical simulation is readily performed with the aid of the high-speed digital computer.
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Ueno, S. Stochastic approach to cauchy system of Chandrasekhar's planetary problem with specular reflector. Astrophys Space Sci 143, 163–173 (1988). https://doi.org/10.1007/BF00636764
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DOI: https://doi.org/10.1007/BF00636764