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Numerical Solutions of a Boundary Value Problem for the Anomalous Diffusion Equation with the Riesz Fractional Derivative

Mariusz Ciesielski·Jacek Leszczynski
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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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Mariusz Ciesielski, Jacek Leszczynski. 2005-06-27. Numerical Solutions of a Boundary Value Problem for the Anomalous Diffusion Equation with the Riesz Fractional Derivative. https://arxiv.org/abs/math/0506556

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