The fundamental and numerical solutions of the Riesz space fractional reaction-dispersion equation

Authors

  • J Chen
  • Fawang Liu
  • Ian Turner
  • Vo Anh

DOI:

https://doi.org/10.21914/anziamj.v50i0.2345

Keywords:

, random walk, fractional derivatives, probability density, stability, convergence

Abstract

A Riesz space-fractional reaction–dispersion equation (RSFRDE) is obtained from the classical reaction–dispersion equation (RDE) by replacing the second-order space derivative with a Riesz derivative of order beta in (1,2]. In this paper, using Laplace and Fourier transforms, we obtain the fundamental solution for a RSFRDE. We propose an explicit finite-difference approximation for a RSFRDE in a bounded spatial domain, and analyse its stability and convergence. Some numerical examples are presented. doi:10.1017/S1446181108000333

Published

2009-09-16

Issue

Section

Articles for Printed Issues