Computational mathematics

On the stability and convergence of difference schemes for the generalized fractional diffusion equation with Robin boundary value conditions

A. K. Bazzaev<sup>ab

a</sup> North-Ossetian State University, 44–46, Vatutina str., Vladikavkaz, 362025, Russia
^b Vladikavkaz Institute of Management, 14, Borodinskaya str., Vladikavkaz, 362025, Russia

Abstract: In this work a difference schemes of higher order approximation are constructed for the generalized diffusion equation of fractional order with the Robin boundary value conditions. Using the maximum principle, we obtain a priori estimates and prove the stability and the uniform convergence of difference schemes.

Keywords: fractional derivative, Caputo fractional derivative, difference schemes, Robin boundary value conditions, maximum principle, convergence and stability.

UDC: 519.633

MSC: 65M12

Received August 28, 2019, published June 4, 2020

DOI: 10.33048/semi.2020.17.053

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