In this paper we present a variational method for approximating solutions of the Dirichlet problem for the neutron transport equation in the stationary case. Error estimates from numerical examples are used to evaluate an approximation of the solution with respect to the steps of two grids.
@article{bwmeta1.element.doi-10_2478_BF02476539,
author = {Olga Martin},
title = {A numerical solution of a two-dimensional transport equation},
journal = {Open Mathematics},
volume = {2},
year = {2004},
pages = {191-198},
zbl = {1105.65113},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_BF02476539}
}
Olga Martin. A numerical solution of a two-dimensional transport equation. Open Mathematics, Tome 2 (2004) pp. 191-198. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_BF02476539/
[1] K.M. Case and P.F. Zweifel: Linear Transport Theory, Addison-Wesley, Massachusetts, 1967.
[2] W.R. Davis: Classical Fields, Particles and the Theory of Relativity, Gordon and Breach, New York, 1970.
[3] S. Glasstone and C. Kilton: The Elements of Nuclear Reactors Theory, Van Nostrand, Toronto-New York-London, 1982.
[4] G. Marchouk: Méthodes de calcul numérique, Édition MIR de Moscou, 1980.
[5] G. Marchouk and V. Shaydourov: Raffinementdes solutions des schémas aux différences, Édition MIR de Moscou, 1983.
[6] G. Marciuk and V. Lebedev: Cislennie metodî v teorii perenosa neitronov, Atomizdat, Moscova, 1971.
[7] O. Martin: “Une méthode de résolution de l'équation du transfert des neutrons”, Rev. Roum. Sci. Tech.-Méc. Appl., Vol. 37, (1992), pp. 623–646.
[8] N. Mihailescu: “Oscillations in the power distribution in a reactor”, Rev. Nuclear Energy, Vol. 9, No. 1-4, (1998), pp. 37–41.
[9] H. Pilkuhn: Relativistic Particle Physics, Springer Verlag, New York-Heidelberg-Berlin, 1980.