Crank-Nicolson method for the fractional diffusion equation with the Riesz fractional derivative

Authors:
Cem Çelik;Melda Duman
Affiliations:
Dokuz Eylül University, Faculty of Science, Department of Mathematics, 35160 Buca, Izmir, Turkey;Dokuz Eylül University, Faculty of Science, Department of Mathematics, 35160 Buca, Izmir, Turkey
Venue:
Journal of Computational Physics
Year:
2012

Citing 6
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Abstract

We examine a numerical method to approximate to a fractional diffusion equation with the Riesz fractional derivative in a finite domain, which has second order accuracy in time and space level. In order to approximate the Riesz fractional derivative, we use the ''fractional centered derivative'' approach. We determine the error of the Riesz fractional derivative to the fractional centered difference. We apply the Crank-Nicolson method to a fractional diffusion equation which has the Riesz fractional derivative, and obtain that the method is unconditionally stable and convergent. Numerical results are given to demonstrate the accuracy of the Crank-Nicolson method for the fractional diffusion equation with using fractional centered difference approach.