MATHEMATICS. MATHEMATIC MODELING

Difference schemes for the equation of heat conduction with a fractional derivative in boundary conditions

A. B. Mambetova

Kabardin-Balkar State University named after H. M. Berbekov, 360004, Nalchik, 173, Chernyshevsky street

Abstract: 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 $0<\alpha<1$) 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.

UDC: 517.949.8

Received: 20.10.2009

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