Numerical simulations of anomalous diffusion

Details Numerical simulations of anomalous diffusion Numerical simulations of anomalous diffusion

2003-09-02

arxiv.org/abs/math-ph/0309007v1

Physics

Mathematical Physics

5 pages, 2 figures, CMM 2003 Conference Gliwice/Wisla Poland

Scientific paper

In this paper we present numerical methods - finite differences and finite elements - for solution of partial differential equation of fractional order in time for one-dimensional space. This equation describes anomalous diffusion which is a phenomenon connected with the interactions within the complex and non-homogeneous background. In order to consider physical initial-value conditions we use fractional derivative in the Caputo sense. In numerical analysis the boundary conditions of first kind are accounted and in the final part of this paper the result of simulations are presented.

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