Numerical Solutions of a Boundary Value Problem for the Anomalous Diffusion Equation with the Riesz Fractional Derivative
Mariusz Ciesielski, Jacek Leszczynski
Abstract
In this paper we present in one-dimensional space a numerical solution of a partial differential equation of fractional order. This equation describes a process of anomalous diffusion. The process arises from the interactions within the complex and non-homogeneous background. We presented a numerical method which bases on the finite differences method. We considered pure initial and boundary-initial value problems for the equation with the Riesz-Feller fractional derivative. In the final part of this paper sample results of simulation were shown.
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