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THE FUNDAMENTAL AND NUMERICAL SOLUTIONS OF THE RIESZ SPACE-FRACTIONAL REACTION–DISPERSION EQUATION

Published online by Cambridge University Press:  01 July 2008

J. CHEN
Affiliation:
School of Science, Jimei University, Xiamen 361021, China
F. LIU*
Affiliation:
School of Mathematical Sciences, Queensland University of Technology, Queensland 4001, Australia (email: [email protected]) School of Mathematical Sciences, South China University of Technology, Guangzhou 510640, China
I. TURNER
Affiliation:
School of Mathematical Sciences, Queensland University of Technology, Queensland 4001, Australia (email: [email protected])
V. ANH
Affiliation:
School of Mathematical Sciences, Queensland University of Technology, Queensland 4001, Australia (email: [email protected])
*
For correspondence; e-mail: [email protected]
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Abstract

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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 β∈(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.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2009

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