Even-odd parity transport equations. 2: The exact characteristic scheme for one-dimensional problems
Matematičeskoe modelirovanie, Tome 26 (2014) no. 7, pp. 33-53.

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

A finite analytic (not the finite difference) characteristic scheme for the even-odd parity transport equations with the algebraic or centered forms of scattering source for plane, cylindrical, or spherical one-dimensional problems is constructed.
Mots-clés : neutron and photon transport equation
Keywords: finite analytic method, characteristic scheme, nuclear reactors, radiative heat transfer.
@article{MM_2014_26_7_a2,
     author = {A. V. Shilkov},
     title = {Even-odd parity transport equations. 2: {The} exact characteristic scheme for one-dimensional problems},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {33--53},
     publisher = {mathdoc},
     volume = {26},
     number = {7},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2014_26_7_a2/}
}
TY  - JOUR
AU  - A. V. Shilkov
TI  - Even-odd parity transport equations. 2: The exact characteristic scheme for one-dimensional problems
JO  - Matematičeskoe modelirovanie
PY  - 2014
SP  - 33
EP  - 53
VL  - 26
IS  - 7
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2014_26_7_a2/
LA  - ru
ID  - MM_2014_26_7_a2
ER  - 
%0 Journal Article
%A A. V. Shilkov
%T Even-odd parity transport equations. 2: The exact characteristic scheme for one-dimensional problems
%J Matematičeskoe modelirovanie
%D 2014
%P 33-53
%V 26
%N 7
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2014_26_7_a2/
%G ru
%F MM_2014_26_7_a2
A. V. Shilkov. Even-odd parity transport equations. 2: The exact characteristic scheme for one-dimensional problems. Matematičeskoe modelirovanie, Tome 26 (2014) no. 7, pp. 33-53. http://geodesic.mathdoc.fr/item/MM_2014_26_7_a2/

[1] Shilkov A. V., “Chetno nechetnye kineticheskie uravneniya perenosa chastits. 1: Algebraicheskaya forma integrala rasseyaniya”, Matematicheskoe modelirovanie, 26:3 (2014), 75–96

[2] Tikhonov A. N., Samarskii A. A., “Odnorodnye raznostnye skhemy vysokogo poryadka tochnosti na neravnomernykh setkakh”, Zhurnal vychislitelnoi matematiki i matematicheskoi fiziki, 1:3 (1961), 425–440 | Zbl

[3] Samarskii A. A., Vvedenie v teoriyu raznostnykh skhem, Nauka, M., 1971, 553 pp. | MR | Zbl

[4] Atkinson F. V., Discrete and continuous boundary problems, Academic Press, New York–London, 1964, 570 pp. | MR | MR | Zbl | Zbl

[5] Ilin A. M., “Raznostnaya skhema dlya differentsialnogo uravneniya s malym parametrom pri starshei proizvodnoi”, Matematicheskie zametki, 6:2 (1969), 237–248 | Zbl

[6] Emelyanov K. V., “Raznostnaya skhema dlya trekhmernogo ellipticheskogo uravneniya s malym parametrom pri starshikh proizvodnykh”, Kraevye zadachi dlya uravnenii matem. fiziki, 11, Sverdlovsk, 1973, 30–42

[7] Chen C. J., Naseri Nashet H., Ho K. S., “Finite analytic numerical solution of heat transfer in two dimensional cavity flow”, Journal of Numerical Heat Transfer, 4 (1981), 179–197

[8] Chen C. J., Chen H. C., “Finite analytic numerical method for unsteady two dimensional Navier–Stokes equations”, Journal of Computational Physics, 53:2 (1984), 209–226 | DOI | Zbl

[9] Lin W., Haik Y., Bernatz R., Chen C. J., “Finite analytic method and its applications: a review”, Dynamics of Atmospheres and Oceans, 27:1 (1998), 17–33 | DOI

[10] Chen C. J., Bernatz R., Carlson K. D., Lin W., Finite analytic method in flows and heat transfer, Taylor and Francis, New York, 2000, 335 pp.

[11] Pontaza J. P., Chen H. C., Reddy J. N., “A local-analytic-based discretization procedure for the numerical solution of incompressible flows”, International Journal for Numerical Methods in Fluids, 49:6 (2005), 657–699 | DOI | MR | Zbl

[12] Liu Z. F., Wang X. H., “Finite analytic numerical method for two-dimensional fluid flow in heterogeneous porous media”, Journal of Computational Physics, 235 (2013), 286–301 | DOI | MR

[13] Goldin V. Ya., Kalitkin N. N., Shishova T. V., “Nelineinye raznostnye skhemy dlya giperbolicheskikh uravnenii”, Zhurnal vychislitelnoi matematiki i matematicheskoi fiziki, 5:5 (1965), 938–944 | MR

[14] Aristova E. N., Modelirovanie vzaimodeistviya izlucheniya s veschestvom, Lambert Academic Publishing, Saabrucken, 2011, 297 pp.

[15] Vladimirov V. S., “Chislennoe reshenie kineticheskogo uravneniya dlya sfery”, Vychislitelnaya matematika, 3, Izd-vo AN SSSR, M., 1958, 3–33

[16] Vladimirov V. S., “Matematika i sozdanie pervykh obraztsov atomnogo oruzhiya”, Atomnaya strategiya, 2009, no. 5 (42), 27–29

[17] Abramov A. A., “Variant metoda progonki”, Zhurnal vychislitelnoi matematiki i matematicheskoi fiziki, 1:2 (1961), 349–351 | MR | Zbl

[18] Marchuk G. I., Metody rascheta atomnykh reaktorov, Atomizdat, M., 1961, 456 pp.

[19] Chetverushkin B. N., Matematicheskoe modelirovanie zadach dinamiki izluchayuschego gaza, Nauka, M., 1985, 304 pp. | Zbl

[20] Richtmyer R. D., Morton K. W., Difference methods for initial-value problems, Interscience Publishers, Wiley Sons, New York–London, 1967 | MR | Zbl