Geodesic
On the numerical solution of the Dirihlets problem for the Poisson's equation with fractional order derivatives
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 2 (2012), pp. 183-187.

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

Difference approximation for the Caputo fractional derivative of the $4-\beta$, $1\beta\leq 2$, order is obtained in the work. The difference schemes for solving the Dirichlet problem for the Poisson equation with fractional derivatives are developed. The right part and initial data stability of difference problem and its convergence are proved.
Mots-clés : Poisson's equation
Keywords: Dirichlet problem, fractional order derivative, numerical method, approximation, difference problem. 
@article{VSGTU_2012_2_a21,
     author = {V. D. Beybalaev},
     title = {On the numerical solution of the {Dirihlets} problem for the {Poisson's} equation with fractional order derivatives},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {183--187},
     publisher = {mathdoc},
     number = {2},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2012_2_a21/}
}
TY  - JOUR
AU  - V. D. Beybalaev
TI  - On the numerical solution of the Dirihlets problem for the Poisson's equation with fractional order derivatives
JO  - Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
PY  - 2012
SP  - 183
EP  - 187
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VSGTU_2012_2_a21/
LA  - ru
ID  - VSGTU_2012_2_a21
ER  - 
%0 Journal Article
%A V. D. Beybalaev
%T On the numerical solution of the Dirihlets problem for the Poisson's equation with fractional order derivatives
%J Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
%D 2012
%P 183-187
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VSGTU_2012_2_a21/
%G ru
%F VSGTU_2012_2_a21
V. D. Beybalaev. On the numerical solution of the Dirihlets problem for the Poisson's equation with fractional order derivatives. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 2 (2012), pp. 183-187. http://geodesic.mathdoc.fr/item/VSGTU_2012_2_a21/

[1] Nakhushev A. M., Fractional calculus and its applications, Fizmatlit, Moscow, 2003, 271 pp. | Zbl

[2] Kol'tsova E. M., Vasilenko V. A., Tarasov V. V., “Numerical methods for solving transport equations in fractal media”, Rus. J. Phys. Chem. A, 74:5 (2000), 848–850

[3] Goloviznin V. M., Korotkin I. A., “Methods for the numerical solution of some one-dimensional equations with fractional derivatives”, Differ. Equ., 42:7 (2006), 967–973 | DOI | MR | Zbl

[4] Tadjeran C., Meerschaert M. M., Scheffler H.-P., “A second-order accurate numerical approximation for the fractional diffusion equation”, J. Comput. Phys., 213:1 (2006), 205–213 | DOI | MR | Zbl

[5] Lynch V. E., Carreras B. A., del-Castillo-Negrete D., Ferreira-Mejias K. M., Hicks H. R., “Numerical methods for the solution of partial differential equations of fractional order”, J. Comput. Phys., 192:2 (2003), 406–421 | DOI | MR | Zbl

[6] Liu Q., Liu F., Turner I., Anh V., “Approximation of the Lévy-Feller advection-dispersion process by random walk and finite difference method”, J. Comput. Phys., 222:1 (2007), 57–70 | DOI | MR | Zbl

[7] Meerschaert M. M., Tadjeran C., “Finite difference approximations for two-sided space-fractional partial differential equations”, Appl. Numer. Math., 56:1 (2006), 80–90 | DOI | MR | Zbl

[8] Beybalaev V. D., “Numerical Method of Solution of the Problem on Transposition of Two-sided Derivative of the Fractional Order”, Vestn. Samar. Gos. Tekhn. Univ. Ser. Fiz.-Mat. Nauki, 2009, no. 1(18), 267–270 | DOI

[9] Beybalayev V. D., “Mathematical model of heat transfer in fractal structure mediums”, Math. Models Comput. Simul., 2:1 (2010), 91–97 | DOI | MR

[10] Samarskiy A. A., Gulin A. V., Numerical methods, Nauka, Moscow, 1989, 432 pp.