Numerical simulations of anomalous diffusion

Abstract

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.

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

References in corpus (1)

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

Cited by in corpus (5)

• Numerical solutions to boundary value problem for anomalous diffusion equation with Riesz-Feller fractional operator
• Numerical treatment of an initial-boundary value problem for fractional partial differential equations
• Numerical Solutions of a Boundary Value Problem for the Anomalous Diffusion Equation with the Riesz Fractional Derivative
• Artificial Neural Network Approach for Solving Fractional order initial value problems
• Monte Carlo Random Walk Simulations Based on Distributed Order Differential Equations