Mathematics
Scientific paper
May 1981
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981ap%26ss..76..441d&link_type=abstract
Astrophysics and Space Science, vol. 76, no. 2, May 1981, p. 441-463.
Mathematics
1
Atmospheric Scattering, Planetary Atmospheres, Radiative Transfer, Transport Theory, Integral Equations, Laplace Transformation, Linear Equations, Operators (Mathematics)
Scientific paper
This paper develops a new exact method combined with finite Laplace transform and theory of linear singular operators to obtain a solution of transport equation in finite plane-parallel steady-state scattering atmosphere both for angular distribution of radiation from the bounding faces of the atmosphere and for intensity of radiation at any depth of the atmosphere. The emergent intensity of radiation from the bounding faces are determined from simultaneous linear integral equations of the emergent intensity of radiation in terms of X and Y equations of Chandrasekhar. The intensity of radiation at any optical depth for a positive and negative direction parameter is derived by inversion of the Laplace transform in terms of integrals of the emergent intensity of radiation. A new expression of the X and Y equation is also derived for easy numerical computation.
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