Geodesic
Difference schemes for the diffusion equation
News of the Kabardin-Balkar scientific center of RAS, no. 2 (2011), pp. 5-9

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In this work the difference scheme for the diffusion equation of fractional order with lumped heat capacity of the boundary conditions is presented. In an a priori estimate for solutions of the difference problem in the uniform metric, which implies the convergence of a solution of the problem to solving the differential problem in the uniform metric speeds $O (h^2/\tau^{\alpha-1} + \tau^{\alpha})$, $h^2 = o(\tau^{\alpha-1})$, where $\tau$, $h$ are grid steps in time and space coordinate.
Keywords: boundary value problem, fractional derivative of Caputo, difference scheme.
Mots-clés : diffusion equation of fractional order 
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     author = {A. B. Mambetova},
     title = {Difference schemes for the diffusion equation},
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A. B. Mambetova. Difference schemes for the diffusion equation. News of the Kabardin-Balkar scientific center of RAS, no. 2 (2011), pp. 5-9. http://geodesic.mathdoc.fr/item/IZKAB_2011_2_a0/