Geodesic
On the determination of optimal nodes and weight factors for the solution of completely incoherent scattering problem
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 13 (2016), pp. 592-598

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For the numerical solution of the radiative transfer equation with complete redistribution of frequencies, it is necessary to select nodes and weight factors close to optimal, which provide the greatest proximity $\delta$ between the exact and approximate solutions. The issue is reduced to a discrete boundary-value problem. We prove the theorem of existence and uniqueness of solution for above discrete boundary-value problem. We show that this solution imparts minimum to the function $\delta.$ At the end of the work we give examples representing interest in radiative transfer theory of light and gamma quanta.
Keywords: weight factors, "shooting" method, existence of the solution, complete redistribution of frequencies.
Mots-clés : nodes, transfer equation 
@article{SEMR_2016_13_a77,
     author = {A. Kh. Khachatryan},
     title = {On the determination of optimal nodes and weight factors for the solution of completely incoherent scattering problem},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {592--598},
     publisher = {mathdoc},
     volume = {13},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2016_13_a77/}
}
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A. Kh. Khachatryan. On the determination of optimal nodes and weight factors for the solution of completely incoherent scattering problem. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 13 (2016), pp. 592-598. http://geodesic.mathdoc.fr/item/SEMR_2016_13_a77/