Integral equations satisfied by the H- X- and Y-functions and the albedo problem

We come back to a nonlinear integral equation satisfied by the function H, which is distinct from the classical H-equation. Established for the first time by Busbridge (1955), it appeared occasionally in the literature since then. First of all, this equation is generalized over the whole complex pla...

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Bibliographic Details
Published in:Journal of quantitative spectroscopy & radiative transfer 2004-06, Vol.86 (2), p.133-150
Main Authors: Rutily, Bernard, Chevallier, Loı̈c, Bergeat, Jacques
Format: Article
Language:English
Subjects:
Albedo problem
Functions H, X and Y
Integral equations
Isotropic scattering
Plane–parallel geometry
Transport (or transfer) theory
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Summary:We come back to a nonlinear integral equation satisfied by the function H, which is distinct from the classical H-equation. Established for the first time by Busbridge (1955), it appeared occasionally in the literature since then. First of all, this equation is generalized over the whole complex plane using the method of residues. Then its counterpart in a finite slab is derived; it consists in two series of integral equations for the X- and Y-functions. These integral equations are finally applied to the solution of the albedo problem in a slab.
ISSN:0022-4073
1879-1352
DOI:10.1016/S0022-4073(03)00279-6