Locally one-dimensional difference schemes for the fractional order diffusion equation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 10, pp. 1878-1887 Cet article a éte moissonné depuis la source Math-Net.Ru

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Locally-one-dimensional difference schemes for the fractional diffusion equation in multidimensional domains are considered. Stability and convergence of locally one-dimensional schemes for this equation are proved.
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M. M. Lafisheva; M. H. Shhanukov-Lafishev. Locally one-dimensional difference schemes for the fractional order diffusion equation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 10, pp. 1878-1887. http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_10_a9/

[1] Dinariev O. Yu., “Filtratsiya v treschinovatoi srede s fraktalnoi geometriei treschin”, Izv. RAN. Mekhan. zhidkosti i gaza, 1990, no. 5, 66–70 | MR | Zbl

[2] Kobelev V. L., Kobelev Ya. L., Romanov E. P., “Nedebaevskaya relaksatsiya i diffuziya v fraktalnom prostranstve”, Dokl. RAN, 361:6 (1998), 755–758 | MR | Zbl

[3] Kobelev V. L., Kobelev Ya. L., Romanov E. P., “Avtovolnovye protsessy pri nelineinoi fraktalnoi diffuzii”, Dokl. RAN, 369:3 (1999), 332–333 | Zbl

[4] Kochubei A. Yu., “Diffuziya drobnogo poryadka”, Differents. ur-niya, 26 (1990), 660–670 | MR

[5] Shogenov V. Kh., Kumykova S. K., Shkhanukov-Lafishev M. Kh., “Obobschennye uravneniya perenosa i drobnye proizvodnye”, Dop. HAH Ukraïni, 1997, no. 12, 47–55 | MR

[6] Barenblatt G. I., Zheltov Yu. P., “Ob osnovnykh uravneniyakh filtratsii odnorodnoi zhidkosti v treschinovatykh porodakh”, Dokl. AN SSSR, 132:3 (1960), 545–548 | Zbl

[7] Nigmatullin P. P., “The realization of generalized transfer equation in a medium with fractal geometry”, Phys. Status Solidi. B, 133 (1986), 425–430 | DOI

[8] Chukbar K. B., “Stokhasticheskii perenos i drobnye proizvodnye”, Zh. eksperim. i teor. fiz., 108:5(11) (1995), 1875–1884

[9] Goloviznin V. M., Kisilev V. P., Korotkii H. A., Chislennye metody resheniya uravneniya diffuzii s drobnoi proizvodnoi v odnomernom sluchae, Preprint IBRAE-2002-01, IBRAE RAN, M., 2002

[10] Goloviznin V. M., Kisilev V. P., Korotkii H. A., Yurkov Yu. P., Nekotorye osobennosti vychislitelnykh algoritmov dlya uravnenii drobnoi diffuzii, Preprint IBRAE-2002-01, IBRAE RAN, M., 2002

[11] Nakhushev A. M., Drobnoe ischislenie i ego primenenie, Fizmatgiz, M., 2003 | Zbl

[12] Samarskii A. A., Teoriya raznostnykh skhem, Nauka, M., 1977 | MR | Zbl

[13] Samarskii A. A., Gulin A. B., Ustoichivost raznostnykh skhem, Nauka, M., 1973 | Zbl