Numerical Solutions of a Boundary Value Problem for the Anomalous Diffusion Equation with the Riesz Fractional Derivative
Numerical Analysis
2007-05-23 v1
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.
Keywords
Cite
@article{arxiv.math/0506556,
title = {Numerical Solutions of a Boundary Value Problem for the Anomalous Diffusion Equation with the Riesz Fractional Derivative},
author = {Mariusz Ciesielski and Jacek Leszczynski},
journal= {arXiv preprint arXiv:math/0506556},
year = {2007}
}
Comments
5 pages, 4 figures, 16th International Conference on Computer Methods in Mechanics CMM-2005, June 21-24, 2005, Czestochowa, Poland