Geodesic
Locally one-dimensional scheme for parabolic equation of general type with nonlocal source
News of the Kabardin-Balkar scientific center of RAS, no. 3 (2017), pp. 5-12.

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

In this work we consider locally one-dimensional scheme for the equation of parabolic type of the gen-eral form in p-dimensional parallelepiped. The a priori estimate for the solution of the locally one-dimensional scheme is obtained.
Keywords: boundary value problem, locally one-dimensional scheme, stability, convergence of a scheme, an a priori estimate, an approximation error. 
@article{IZKAB_2017_3_a0,
     author = {Z. V. Beshtokova},
     title = {Locally one-dimensional scheme for parabolic equation of general type with nonlocal source},
     journal = {News of the Kabardin-Balkar scientific center of RAS},
     pages = {5--12},
     publisher = {mathdoc},
     number = {3},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IZKAB_2017_3_a0/}
}
TY  - JOUR
AU  - Z. V. Beshtokova
TI  - Locally one-dimensional scheme for parabolic equation of general type with nonlocal source
JO  - News of the Kabardin-Balkar scientific center of RAS
PY  - 2017
SP  - 5
EP  - 12
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IZKAB_2017_3_a0/
LA  - ru
ID  - IZKAB_2017_3_a0
ER  - 
%0 Journal Article
%A Z. V. Beshtokova
%T Locally one-dimensional scheme for parabolic equation of general type with nonlocal source
%J News of the Kabardin-Balkar scientific center of RAS
%D 2017
%P 5-12
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IZKAB_2017_3_a0/
%G ru
%F IZKAB_2017_3_a0
Z. V. Beshtokova. Locally one-dimensional scheme for parabolic equation of general type with nonlocal source. News of the Kabardin-Balkar scientific center of RAS, no. 3 (2017), pp. 5-12. http://geodesic.mathdoc.fr/item/IZKAB_2017_3_a0/

[1] L. I. Kamynin, “Ob odnoi kraevoi zadache teorii teploprovodnosti s neklassicheskimi granichnymi usloviyami”, Zh. vychis. matem. i matem. fiz, 4:6 (1964), 1006–1023

[2] L. F. Chudnovskii, “Nekotorye korrektivy v postanovke i reshenii zadach teplo- i vlagoperenosa v pochve”, Sbornik trudov po agrofizike, v. 23, Gidrometeoizdat, 1969, 41–54

[3] A. V. Bitsadze, A. A. Samarskii, “O nekotorykh prosteishikh obobscheniyakh lineinykh ellipticheskikh kraevykh zadach”, Dokl. AN SSSR, 185:4, 739–740 | MR | Zbl

[4] N. N. Ionkin, “Reshenie odnoi kraevoi zadachi v teorii teploprovodnosti s nelokalnym usloviem”, Differents. uravn., 13:2 (1977), 239–304

[5] N. N. Ionkin, O ravnomernoi skhodimosti raznostnoi skhemy dlya odnoi nestatsionarnoi nelokalnoi kraevoi zadachi. Aktualnye voprosy prikladnoi matematiki, Iz-vo MGU, M., 1989, 240 pp.

[6] N. N. Ionkin, E. I. Moiseev, “O zadache dlya uravneniya teploprovodnosti s dvutochechnymi kraevymi usloviyami”, Differents. uravn., 15:7 (1979), 1284–1295 | MR | Zbl

[7] V. A. Ilin, E. I. Moiseev, “Nelokalnaya zadacha dlya operatora Shturma-Liuvillya v diffe-rentsialnoi i raznostnoi traktovkakh”, Dokl. AN SSSR, 291:3 (1986), 534–539 | MR

[8] D. G. Gordeziani, O metodakh resheniya odnogo klassa nelokalnykh kraevykh zadach, Preprint instituta prikladnoi matematiki pri TGU, Tbilisi, 1981

[9] A. M. Nakhushev, “Nelokalnaya zadacha i zadacha Gursa dlya nagruzhennogo uravneniya giperbolicheskogo tipa i ikh prilozheniya k prognozu pochvennoi vlagi”, Dokl. AN SSSR, 242:5 (1979), 1008–1011

[10] A. P. Soldatov, M. Kh. Shkhanukov, “Kraevye zadachi s obschim nelokalnym usloviem Samarskogo A.A. dlya psevdoparabolicheskogo uravneniya vysokogo poryadka”, Dokl. AN SSSR, 297:3 (1987), 547–552

[11] A. I. Kozhanov, “Ob odnoi nelokalnoi kraevoi zadache s peremennymi koeffitsientami dlya uravnenii teploprovodnosti i Allera”, Differents. uravn, 40:6 (2004), 763–774 | MR | Zbl

[12] A. A. Samarskii, Teoriya raznostnykh skhem, Nauka, M., 1983, 656 pp.

[13] V. B. Andreev, “O skhodimosti raznostnykh skhem, approksimiruyuschikh vtoruyu i tretyu kraevye zadachi dlya ellipticheskikh uravnenii”, Zh. vychisl. matem. i matem. fiz, 8:6 (1968), 1218–1231 | Zbl

[14] A. A. Samarskii, A. V. Gulin, Ustoichivost raznostnykh skhem, Nauka, M., 1973, 480 pp.

[15] A. K. Bazzaev, D. K. Gutnova, M. Kh. Shkhanukov-Lafishev, “Lokalno-odnomernaya skhema dlya parabolicheskogo uravneniya s nelokalnym usloviem”, Zh. vychisl. matem. i matem. fiz., 52 (2012), 1048–1057 | Zbl