M. H. Shhanukov-Lafishev, A. R. Bechelova, Z. V. Beshtokova, “Convergence of difference schemes for the diffusion equation in porous media with structures having fractal geometry”, News of the Kabardin-Balkar scientific center of RAS, 2014, Issue 5,Pages <nobr>17

MATHEMATICS. MATHEMATIC MODELING

Convergence of difference schemes for the diffusion equation in porous media with structures having fractal geometry

M. H. Shhanukov-Lafishev^a, A. R. Bechelova^b, Z. V. Beshtokova^b

^a Institute of Computer Science and Problems of Regional Management of KBSC of the Russian Academy of Sciences, 360000, KBR, Nalchik, 37-a, I. Armand street
^b Kabardin-Balkar State University named after H. M. Berbekov, 360004, KBR, Nalchik, 173, Chernyshevsky street

Abstract: In this paper a priori estimate , which implies the convergence of a solution of the problem to the solution of the differential problem in the uniform metric with speed $O(h^2+\tau)$ is acquired by the method of stationary perturbations.

Keywords: differential equation of diffusion, existence and uniqueness, a priori estimate, unique solvability and convergence.

UDC: 514.7

Received: 02.06.2014