Mathematics
Scientific paper
Dec 1985
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985jqsrt..34..473c&link_type=abstract
Journal of Quantitative Spectroscopy and Radiative Transfer (ISSN 0022-4073), vol. 34, Dec. 1985, p. 473-485.
Mathematics
5
Fredholm Equations, Numerical Integration, Radiative Transfer, Scattering, Singular Integral Equations, Collimation, Isotropy, Linear Equations, Optical Thickness, Reflectance, Singularity (Mathematics), Transmittance
Scientific paper
A numerical procedure for solving a singular Fredholm integral equation, which describes radiative transfer in an absorbing and isotropically scattering layer exposed to collimated radiation, is studied. The integral equation is solved by subtracting out the singularity and then approximating the integral term by a Gaussian quadrature. Bidirectional and hemispherical properties are found from the source function. Any arbitrary directional distribution of incident radiation can be handled by superimposing the collimated radiation case. In particular, the case of isotropic incident radiation is presented. The method gives accurate results, even for the extreme conditions of large optical thickness and large angle of incidence.
Crosbie A. L.
Pattabongse M.
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