Computational mathematics

Locally one-dimensional difference schemes for the fractional diffusion equation with a fractional derivative in lowest terms

A. K. Bazzaev^ab, I. D. Tsopanov<sup>b

a</sup> North-Ossetia State University, Vladikavkaz
^b Vladikavkaz Institute of Management

Abstract: For a fractional diffusion equation with a fractional derivative in lowest terms with Robin boundary conditions, locally one-dimensional difference schemes are considered and their stability and convergence are proved.

Keywords: locally one-dimensional difference scheme, slow diffusion equation, Caputo fractional derivative, maximum principle, stability and convergence of difference schemes, Robin boundary conditions.

UDC: 519.633

MSC: 65M06

Received November 18, 2014, published February 2, 2015

DOI: 10.17377/semi.2015.12.007