Difference methods for solving boundary value problems for fractional differential equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 10, pp. 1871-1881 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Difference schemes for second-order ordinary and partial differential equations with a fractional time derivative are considered. Stationary and nonstationary problems for the diffusion equation in one-and multidimensional domains are examined separately. The stability and convergence of the difference schemes for these equations are proved.
@article{ZVMMF_2006_46_10_a13,
     author = {F. I. Taukenova and M. H. Shhanukov-Lafishev},
     title = {Difference methods for solving boundary value problems for fractional differential equations},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1871--1881},
     year = {2006},
     volume = {46},
     number = {10},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_10_a13/}
}
TY  - JOUR
AU  - F. I. Taukenova
AU  - M. H. Shhanukov-Lafishev
TI  - Difference methods for solving boundary value problems for fractional differential equations
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2006
SP  - 1871
EP  - 1881
VL  - 46
IS  - 10
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_10_a13/
LA  - ru
ID  - ZVMMF_2006_46_10_a13
ER  - 
%0 Journal Article
%A F. I. Taukenova
%A M. H. Shhanukov-Lafishev
%T Difference methods for solving boundary value problems for fractional differential equations
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2006
%P 1871-1881
%V 46
%N 10
%U http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_10_a13/
%G ru
%F ZVMMF_2006_46_10_a13
F. I. Taukenova; M. H. Shhanukov-Lafishev. Difference methods for solving boundary value problems for fractional differential equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 10, pp. 1871-1881. http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_10_a13/

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

[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] Goloviznin V. M., Kisilev V. P., Korotkin I. A., Chislennye metody resheniya uravneniya diffuzii s drobnoi proizvodnoi v odnomernom sluchae, Preprint No IBRAE-2003-12, IBRAE RAN, M., 2003, 35 pp.

[5] Goloviznin V. M., Kisilev V. P., Korotkin I. A., Yurkov Yu. I., “Pryamye zadachi neklassicheskogo perenosa radionuklidov v geologicheskikh formatsiyakh”, Izv. RAN. Energetika, 2004, no. 4, 121–130

[6] Nigmatullin P. P., “Osobennosti relaksatsii sistemy s “ostatochnoi” pamyatyu”, Fiz. tverdogo tela, 27:5 (1985), 1583–1585

[7] L. Petronero, E. Tozatti (red.), “Fraktaly v fizike”, Tr. VI Mezhdunar. simpoziuma po fraktalam v fiz. (MTsTF, Triest, Italiya, 9–12 iyulya 1985), Mir, M., 1988 | MR

[8] Mandelbrojt B. B., The fractal geometry of nature, Freeman, San-Francisco, 1983

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

[10] Samko S. G., Kilbas A. A., Marichev O. I., Integraly i proizvodnye drobnogo poryadka i nekotorye ikh prilozheniya, Nauka i tekhn., Minsk, 1987 | MR | Zbl

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

[12] Gekkieva S. Kh., “Kraevaya zadacha dlya obobschennogo uravneniya perenosa s drobnoi proizvodnoi po vremeni”, Dokl. Adygskoi (Cherkesskoi) mezhdunar. akad. nauk, 1:1 (1994), 17–19 | MR

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

[14] Kumykova S. K., “Ob odnoi kraevoi zadache dlya uravneniya $\mathrm{sign}y^m u_{xx}+u_{uu}=0$”, Differents. ur-niya, 12:1 (1976), 79–88 | MR | Zbl

[15] Nakhushev A. M., Drobnoe ischislenie i ego primenenie, Fizmatlit, M., 2003 | Zbl

[16] Ladyzhenskaya O. A., Kraevye zadachi matematicheskoi fiziki, Nauka, M., 1973 | MR

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

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

[19] Shkhanukov M. X., “O skhodimosti raznostnykh skhem dlya differentsialnykh uravnenii s drobnoi proizvodnoi”, Dokl. RAN, 348:6 (1996), 746–748 | MR | Zbl