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

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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. 
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     title = {Difference schemes for the equation of heat},
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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/