Geodesic
Exponential finite-difference schemes with double integral transformation for desicion of diffusion-convection equations
Matematičeskoe modelirovanie, Tome 24 (2012) no. 12, pp. 29-32.

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

Object of this research are differential equations of diffusion-convection type. These equations are used for the description of many nonlinear processes in solids, liquids and gases. Despite a set of works on problems of their decision, they still present certain difficulties for the theoretical and numerical analysis. In the work the grid approach on the basis of the finite differences method for the solution of the equations of this kind is considered. For simplification of consideration the one-dimensional version of the equation was chosen. However the main properties of the equation are equal non-monotonicity and non-linearity were kept. For the solution of boundary problems for such equations the special variant of non-monotonic sweep procedure is offered.
Mots-clés : diffusion-convection equation
Keywords: finite-difference schemes, integral transformation, algorithm of non-monotonic sweep procedure. 
@article{MM_2012_24_12_a4,
     author = {S. V. Polyakov},
     title = {Exponential finite-difference schemes with double integral transformation for desicion of diffusion-convection equations},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {29--32},
     publisher = {mathdoc},
     volume = {24},
     number = {12},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2012_24_12_a4/}
}
TY  - JOUR
AU  - S. V. Polyakov
TI  - Exponential finite-difference schemes with double integral transformation for desicion of diffusion-convection equations
JO  - Matematičeskoe modelirovanie
PY  - 2012
SP  - 29
EP  - 32
VL  - 24
IS  - 12
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2012_24_12_a4/
LA  - ru
ID  - MM_2012_24_12_a4
ER  - 
%0 Journal Article
%A S. V. Polyakov
%T Exponential finite-difference schemes with double integral transformation for desicion of diffusion-convection equations
%J Matematičeskoe modelirovanie
%D 2012
%P 29-32
%V 24
%N 12
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2012_24_12_a4/
%G ru
%F MM_2012_24_12_a4
S. V. Polyakov. Exponential finite-difference schemes with double integral transformation for desicion of diffusion-convection equations. Matematičeskoe modelirovanie, Tome 24 (2012) no. 12, pp. 29-32. http://geodesic.mathdoc.fr/item/MM_2012_24_12_a4/

[1] Samarskii A. A., Mikhailov A. P., Matematicheskoe modelirovanie, Nauka. Fizmatlit, M., 1997, 320 pp.

[2] Samarskii A. A., “O monotonnykh raznostnykh skhemakh dlya ellipticheskikh i parabolicheskikh uravnenii v sluchae nesamosopryazhennogo ellipticheskogo operatora”, ZhVMiMF, 5:3 (1965), 548–551 | MR

[3] Golant E. I., “O sopryazhennykh semeistvakh raznostnykh skhem dlya uravnenii parabolicheskogo tipa s mladshimi chlenami”, ZhVMiMF, 18:5 (1978), 1162–1169 | MR | Zbl

[4] Karetkina N. V., “Bezuslovno ustoichivaya raznostnaya skhema dlya parabolicheskikh uravnenii, soderzhaschikh pervye proizvodnye”, ZhVMiMF, 20:1 (1980), 236–240 | MR | Zbl

[5] Fryazinov I. V., “Metod balansa i variatsionno-raznostnye skhemy”, Dif. uravn., 16:7 (1980), 1332–1343 | MR | Zbl

[6] Polyakov S. V., Sablikov V. A., “Lateralnyi perenos fotoindutsirovannykh nositelei zaryada v geterostrukturakh s dvumernym elektronnym gazom”, Matem. model., 9:12 (1997), 76–86 | Zbl

[7] Kudryashova T. A., Polyakov S. V., “O nekotorykh metodakh resheniya kraevykh zadach na mnogoprotsessornykh vychislitelnykh sistemakh”, Trudy chetvertoi mezhdunarodnoi konferentsii po matematicheskomu modelirovaniyu (27 iyunya–1 iyulya 2000, g. Moskva), v. 2, ed. L. A. Uvarova, Izd-vo “STANKIN”, M., 2001, 134–145

[8] Polyakov S. V., “Eksponentsialnye skhemy dlya resheniya evolyutsionnykh uravnenii na neregulyarnykh setkakh”, Uchenye zapiski kazanskogo gosudarstvennogo universiteta. Seriya “Fiziko-matematicheskie nauki”, 149, no. 4, 2007, 121–131

[9] Karamzin Yu. N., Polyakov S. V., “Eksponentsialnye konechno-ob'ëmnye skhemy dlya resheniya ellipticheskikh i parabolicheskikh uravnenii obschego vida na neregulyarnykh setkakh”, Setochnye metody dlya kraevykh zadach i prilozheniya, Materialy Vosmoi Vserossiiskoi konferentsii, posvyaschennoi 80-letiyu so dnya rozhdeniya A. D. Lyashko, Kazanskii universitet, Kazan, 2010, 234–248

[10] Samarskii A. A., Vvedenie v teoriyu raznostnykh skhem, Nauka, M., 1971, 552 pp. | MR | Zbl