Geodesic
A new version of the discrete ordinate method for the calculation of the intrinsic radiation in horizontally homogeneous atmospheres
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 10, pp. 1741-1755

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A new version of the discrete ordinate method for the calculation of the transfer of monochromatic radiation in a scattering, absorbing, and emitting plane-parallel atmosphere of Earth and other planets is proposed. A feature of this version is that the system of linear equations obtained by the discrete ordinate method is solved using the block elimination method. This is an exact and computationally efficient method; moreover it is easy to implement. The computer program developed based on this method is about two times faster than the program used in the free DISORT package. 
@article{ZVMMF_2015_55_10_a11,
     author = {N. I. Ignat'ev and I. V. Mingalev and A. V. Rodin and E. A. Fedotova},
     title = {A new version of the discrete ordinate method for the calculation of the intrinsic radiation in horizontally homogeneous atmospheres},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1741--1755},
     publisher = {mathdoc},
     volume = {55},
     number = {10},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_10_a11/}
}
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N. I. Ignat'ev; I. V. Mingalev; A. V. Rodin; E. A. Fedotova. A new version of the discrete ordinate method for the calculation of the intrinsic radiation in horizontally homogeneous atmospheres. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 10, pp. 1741-1755. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_10_a11/