ANZIAM J. 47(EMAC2005) pp.C48--C68, 2006.

A fractional-order implicit difference approximation for the space-time fractional diffusion equation

F. Liu

P. Zhuang

V. Anh

I. Turner
(received 14 October 2005; revised 4 June 2006)

Abstract

We consider a space-time fractional diffusion equation on a finite domain. The equation is obtained from the standard diffusion equation by replacing the second order space derivative by a Riemann--Liouville fractional derivative of order between one and two, and the first order time derivative by a Caputo fractional derivative of order between zero and one. A fractional order implicit finite difference approximation for the space-time fractional diffusion equation with initial and boundary values is investigated. Stability and convergence results for the method are discussed, and finally, some numerical results show the system exhibits diffusive behaviour.

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Authors

F. Liu
P. Zhuang
School of Mathematical Sciences, Xiamen University, Xiamen 361005, China. mailto:fwliu@xmu.edu.cn, mailto:zxy1104@xmu.edu.cn
V. Anh
I. Turner
School of Mathematical Sciences, Queensland University of Technology, Qld 4001, Australia. mailto:v.anh@qut.edu.au, mailto:i.turner@qut.edu.au

Published June 23, 2006; amended June 26, 2006. ISSN 1446-8735

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Copyright Austral. Mathematical Soc.; prepared June 26, 2006, from Liu.tex with anziamje.sty (v2.4)