Abstract:
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, diffusion equation of fractional order, fractional derivative of Caputo, difference scheme.
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