In this paper, the non-standard finite difference method (NSFDM) is presented for solving numerically the two-dimensional space fractional diffusion equation (SFDE), where the fractional derivative is defined in the sense of the right-shifted Gr¨unwald. The stability and the error analysis for the proposed method are given. Two numerical test examples are presented. It is concluded that the NSFDM scheme preserves numerical stability in larger regions than the standard finite difference method (SFDM).
Hassan Sweilam, Nasser and Faraj Almajbri, Tebra
"Large Stability Regions Method for the Two-dimensional Fractional Diffusion Equation,"
Progress in Fractional Differentiation & Applications: Vol. 1
, Article 6.
Available at: https://dc.naturalspublishing.com/pfda/vol1/iss2/6