Geodesic
Difference schemes for the equation of heat
News of the Kabardin-Balkar scientific center of RAS, no. 1 (2010), pp. 146-150.

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

In this work the author presented the boundary value problem for a heat conduction equation with a fractional derivative in boundary conditions. The equation of parabolic type with variable factors and a fractional derivative on time in boundary conditions (the concept of a fractional derivative of Riemann - Liouville is used at $0\alpha1$) is considered. For this problem the a priori estimation is obtained from which the solution stability on input data and uniqueness follows. The discrete analogue of a problem is constructed, the approximation error is investigated, and also the stability and convergence of the difference scheme are proved.
Keywords: boundary value problem, heat conduction equation, fractional derivative, derivative of Riemann – Liouville, the discrete analogue. 
@article{IZKAB_2010_1_a1,
     author = {A. B. Mambetova},
     title = {Difference schemes for the equation of heat},
     journal = {News of the Kabardin-Balkar scientific center of RAS},
     pages = {146--150},
     publisher = {mathdoc},
     number = {1},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IZKAB_2010_1_a1/}
}
TY  - JOUR
AU  - A. B. Mambetova
TI  - Difference schemes for the equation of heat
JO  - News of the Kabardin-Balkar scientific center of RAS
PY  - 2010
SP  - 146
EP  - 150
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IZKAB_2010_1_a1/
LA  - ru
ID  - IZKAB_2010_1_a1
ER  - 
%0 Journal Article
%A A. B. Mambetova
%T Difference schemes for the equation of heat
%J News of the Kabardin-Balkar scientific center of RAS
%D 2010
%P 146-150
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IZKAB_2010_1_a1/
%G ru
%F IZKAB_2010_1_a1
A. B. Mambetova. Difference schemes for the equation of heat. News of the Kabardin-Balkar scientific center of RAS, no. 1 (2010), pp. 146-150. http://geodesic.mathdoc.fr/item/IZKAB_2010_1_a1/

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

[2] A. M. Nakhushev, Drobnoe ischislenie i ego primenenie, Fizmatlit, M., 2003

[3] A. A. Samarskii, Teoriya raznostnykh skhem, Nauka., M., 1977

[4] F. I. Taukenova, M. Kh. Shkhanukov-Lafishev, “Raznostnye metody resheniya kraevykh zadach dlya differentsialnykh uravnenii drobnogo poryadka”, Vychisl. matem. i matem. fiz, 46:1 (2006), 1871–1881 | MR