Geodesic
On the accuracy of the projection computation of the collision integral
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 4, pp. 697-719 
Yu. A. Anikin. On the accuracy of the projection computation of the collision integral. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 4, pp. 697-719. http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_4_a9/
@article{ZVMMF_2012_52_4_a9,
     author = {Yu. A. Anikin},
     title = {On the accuracy of the projection computation of the collision integral},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {697--719},
     year = {2012},
     volume = {52},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_4_a9/}
}
TY  - JOUR
AU  - Yu. A. Anikin
TI  - On the accuracy of the projection computation of the collision integral
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2012
SP  - 697
EP  - 719
VL  - 52
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_4_a9/
LA  - ru
ID  - ZVMMF_2012_52_4_a9
ER  - 
%0 Journal Article
%A Yu. A. Anikin
%T On the accuracy of the projection computation of the collision integral
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2012
%P 697-719
%V 52
%N 4
%U http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_4_a9/
%G ru
%F ZVMMF_2012_52_4_a9

Voir la notice de l'article provenant de la source Math-Net.Ru

The accuracy of the projection method as applied to the computation of the collision integral is analyzed. It is shown that the method has an error of the second order of smallness with respect to the mesh size. An optimal method for choosing additional nodes that minimizes the computational error is found. The theoretical conclusions and the optimality of the method are confirmed in a series of numerical experiments.

[1] Cheremisin F. G., “A conservative method for calculation of the Boltzmann collision integral”, Doklady Physics, 42:11 (1997), 607–610 | MR

[2] Tcheremissine F. G., “Solution to the Boltzmann kinetic equation for high-Speed flows”, Comp. Math. Math. Phys., 46:2 (2006), 315–329 | DOI | MR | Zbl

[3] Yoshio Sone, Molecular gas dynamics, Birkhauser, Boston, 2007 | MR

[4] Rogier F., Schnider J., “A direct method for solving the Boltzmann equation”, Transport Theory Stat. Phys., 23 (1994), 1–3 | DOI | MR | Zbl

[5] Sobol I. M., Chislennye metody Monte-Karlo, Nauka, M., 1973 | MR

[6] Landau L. D., Lifshits E. M., Teoreticheskaya fizika, v. 10, Fizmatlit, M., 2001

[7] Korobov N. M., Trigonometricheskie summy i ikh prilozheniya, Nauka, M., 1989 | MR | Zbl