Stability and Convergence of an Implicit Difference Approximation for the Space Riesz Fractional Reaction-Dispersion Equation

Jinghua Chen 1*, Fawang Liu 2

1 College of Mathematics, Jimei University, Xiamen 361021, China
2 School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, Qld. 4001, Australia

Received January 1, 2006; Accepted (in revised version) September 8, 2006
Abstract

In this paper, we consider a Riesz space-fractional reaction-dispersion equation (RSFRDE). The RSFRDE is obtained from the classical reaction-dispersion equation by replacing the second-order space derivative with a Riesz derivative of order $\beta\in (1,2].$ We propose an implicit finite difference approximation for RSFRDE. The stability and convergence of the finite difference approximations are analyzed. Numerical results are found in good agreement with the theoretical analysis.

Key words: Riesz fractional derivative; fractional reaction-dispersion equation; implicit finite difference approximation; stability; convergence.

AMS subject classifications: 26A33, 35K57, 65M12

Correspondence to: Jinghua Chen , College of Mathematics, Jimei University, Xiamen 361021, China Email: cjhdzdz@163.com