Geodesic
Pollution spreading in liquid crystals in the electric field
Matematičeskoe modelirovanie, Tome 16 (2004) no. 1, pp. 3-11.

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The results of numerical solution of the convection-diffusion problem with mixed derivatives are presented. These problems appear in the medium with different properties in some directions (e.a. liquid crystals). Mathematical model of pollution spreading in liquid crystals is offered in the paper. Discrete model has got on the base of finite-difference approximations. Iterative methods are used for solution of grid elliptic problems. 
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L. A. Krukier; T. S. Martynova. Pollution spreading in liquid crystals in the electric field. Matematičeskoe modelirovanie, Tome 16 (2004) no. 1, pp. 3-11. http://geodesic.mathdoc.fr/item/MM_2004_16_1_a0/

[1] Pikin S. A., Strukturnye prevrascheniya v zhidkikh kristallakh, Nauka, M., 1981, 336 pp.

[2] Pikin S. A., Blinov L. M., Zhidkie kristally, Nauka, M., 1982, 280 pp.

[3] Landau L. D., Lifshits E. M., Elektrodinamika sploshnykh sred, Nauka, M., 1982, 623 pp. | MR

[4] Landau L. D., Lifshits E. M., Mekhanika sploshnykh sred, Nauka, M., 1986, 736 pp. | MR

[5] Levin V. T., Fiziko-khimicheskaya gidrodinamika, Izd-vo AN SSSR, M., 1952, 538 pp.

[6] Marchuk G. I., Metody vychislitelnoi matematiki, Nauka, M., 1989, 456 pp. | MR

[7] Krukier L. A., “Neyavnye raznostnye skhemy i iteratsionnyi metod ikh resheniya dlya odnogo klassa sistem kvazilineinykh uravnenii”, Izvestiya VUZov, Matem., 1979, no. 7, 41–52 | MR | Zbl

[8] Samarskii A. A., Teoriya raznostnykh skhem, Nauka, M., 1989, 616 pp. | MR

[9] Krukier L. A., Martynova T. S., “O vliyanii formy zapisi uravneniya konvektsii-diffuzii na skhodimost metoda verkhnei relaksatsii”, ZhVM i MF, 39:11 (1999), 1821–1827 | MR | Zbl

[10] Samarskii A. A., Vabischevich P. N., Chislennye metody resheniya zadach konvektsii-diffuzii, EditorialURSS, M., 1999, 248 pp.

[11] Krukier L. A., Martynova T. S., “Reshenie ellipticheskikh kraevykh zadach vtorogo poryadka s malym parametrom pri starshei proizvodnoi iteratsionnymi metodami SOR i SSOR”, Sovr. problemy mat. modelirovaniya, izd-vo RGU, Rostov-na-Donu, 1997, 71–76

[12] Krukier L. A., Martynova T. S., “Point SOR and SSOR methods for the numerical solution of the steady convection-diffusion equation with dominant convection”, Series in Computational and Applied Mathematics IMACS, 5 (1999), 399–404

[13] Bochev M. A., Krukier L. A., “Ob iteratsionnom reshenii silno nesimmetrichnykh sistem lineinykh algebraicheskikh uravnenii”, ZhVM i MF, 37:11 (1997), 1283–1293 | MR | Zbl

[14] Martynova T. S., Belokon T. V., “Non-stationary iterative method for strongly nonsymmetric linear equation systems”, Mat. Modelirovanie, 13:3 (2001), 61–68 | MR | Zbl

[15] Krukier L. A., Chikina L. G., “Kososimmetricheskii iteratsionnyi metod dlya resheniya statsionarnogo uravneniya konvektsii-diffuzii”, Izvestiya VUZov, Matem., 2000, no. 11, 62–75 | MR | Zbl