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

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.

5 pages, 4 figures, 16th International Conference on Computer Methods in Mechanics CMM-2005, June 21-24, 2005, Czestochowa, Poland

References in corpus (2)

• The fundamental solution of the space-time fractional diffusion equation
• Numerical simulations of anomalous diffusion

Cited by in corpus (1)

• Numerical solutions to boundary value problem for anomalous diffusion equation with Riesz-Feller fractional operator