Geodesic
Iterative approximate method of non-linear multidimensional electro-thermal field problems solving
Matematičeskoe modelirovanie, Tome 21 (2009) no. 6, pp. 110-120 
S. A. Gorbatkov; D. V. Polupanov. Iterative approximate method of non-linear multidimensional electro-thermal field problems solving. Matematičeskoe modelirovanie, Tome 21 (2009) no. 6, pp. 110-120. http://geodesic.mathdoc.fr/item/MM_2009_21_6_a9/
@article{MM_2009_21_6_a9,
     author = {S. A. Gorbatkov and D. V. Polupanov},
     title = {Iterative approximate method of non-linear multidimensional electro-thermal field problems solving},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {110--120},
     year = {2009},
     volume = {21},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2009_21_6_a9/}
}
TY  - JOUR
AU  - S. A. Gorbatkov
AU  - D. V. Polupanov
TI  - Iterative approximate method of non-linear multidimensional electro-thermal field problems solving
JO  - Matematičeskoe modelirovanie
PY  - 2009
SP  - 110
EP  - 120
VL  - 21
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/MM_2009_21_6_a9/
LA  - ru
ID  - MM_2009_21_6_a9
ER  - 
%0 Journal Article
%A S. A. Gorbatkov
%A D. V. Polupanov
%T Iterative approximate method of non-linear multidimensional electro-thermal field problems solving
%J Matematičeskoe modelirovanie
%D 2009
%P 110-120
%V 21
%N 6
%U http://geodesic.mathdoc.fr/item/MM_2009_21_6_a9/
%G ru
%F MM_2009_21_6_a9

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

It is proposed an effective approximate method of non-linear multidimensional boundary problems solving. They are shown mathematical substantiation and numerical method approbation.

[1] Ladyzhenskaya O. A., Solonnikov V. A., Uraltseva N. N., Lineinye i kvazilineinye uravneniya parabolicheskogo tipa, Nauka, M., 1967, 736 pp. | MR

[2] Gorbatkov S. A., Gzhivachevski M., “K analizu itero-approksimativnogo metoda dlya trekhmernykh zadach teploprovodnosti”, Izvestiya AN SSSR. Energetika i transport, 1988, no. 2, 101–110 | Zbl

[3] Badamshin R. A., Gorbatkov S. A., Klestov E. A., Optimalnoe terminalnoe upravlenie sistemami s raspredelennymi parametrami pri nepolnom izmerenii ikh sostoyaniya, Ufimskii gosud. aviats. tekhnich. un-t, Ufa, 1997, 313 pp.

[4] Badamshin R. A., Gorbatkov S. A., Melnikov V. I., “Numeral Methods of Optimizing the Distribution of 2- and 3-dimential Electromagnetic and Heat Field”, 40 Internationales Wissenschaftiches Kolloqium, Vortage. Band 2 (18–21.09.1995, Ilmenau, FRG), Technische Universitat Ilmenau, Ilmenau, 1995, 318–323

[5] Nikolskii S. M., Priblizhenie funktsii mnogikh peremennykh i teoremy vlozheniya, Nauka, M., 1969, 480 pp. | MR

[6] Galitsyn A. S., Zhukovskii A. N., Integralnye preobrazovaniya i spetsialnye funktsii v zadachakh teploprovodnosti, Naukova dumka, Kiev, 1976, 268 pp.

[7] Aizen A. M., Redchits I. S., Fedotkin I. M., “Ob uluchshenii skhodimosti ryadov, vkhodyaschikh v resheniya uravnenii teploprovodnosti”, Inzh. fiz. zhurnal, 26:4 (1974), 659–666 | MR

[8] Ortega Dzh., Reinboldt R., Iteratsionnye metody resheniya nelineinykh sistem uravnenii so mnogimi neizvestnymi, Mir, M., 1975, 560 pp. | MR

[9] Kantorovich L. V., Akilov G. P., Funktsionalnyi analiz, Mir, M., 1977, 742 pp. | MR

[10] Fedorenko R. P., “Iteratsionnye metody resheniya raznostnykh ellipticheskikh uravnenii”, UMN, 28:2(170) (1973), 121–182 | MR | Zbl

[11] Bakharev I. A., Gzhivachevski M., Gorbatkov S. A., Melnikov V. I., “Razrabotka raznostnykh skhem dlya rascheta dvukh- i trekhmernykh elektromagnitnykh polei”, Elektrodinamika SVCh i KVCh. Teoriya, matematicheskoe modelirovanie i SAPR OIS SVCh, Mezhvuzovskii sbornik nauchnykh trudov, Institut avtomatizatsii proektirovaniya AN SSSR, M., 1991, 53–65

[12] Galushkin A. I., Sudarikov V. V., Shabanov E. V., “Neiromatematika: metody resheniya zadach na neirokompyuterakh”, Matematicheskoe modelirovanie, 3:8 (1991), 93–111 | MR

[13] Gorbachenko V. I., Neirokompyutery v reshenii kraevykh zadach teorii polya, Radiotekhnika, M., 2003, 336 pp.

[14] Tarkhov D. A., Neironnye seti kak sredstvo matematicheskogo modelirovaniya, Radiotekhnika, M., 2006, 48 pp.