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Analytical and numerical solutions for the time and space-symmetric fractional diffusion equation

Yang, Qianqian, Turner, Ian, & Liu, Fawang (2008) Analytical and numerical solutions for the time and space-symmetric fractional diffusion equation. In ANZIAM Journal : Proceedings of the 4th Biennial Computational Techniques and Applications Conference (CTAC2008), Australian National University, Canberra, C800-C814.

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    Abstract

    We consider a time and space-symmetric fractional diffusion equation (TSS-FDE) under homogeneous Dirichlet conditions and homogeneous Neumann conditions. The TSS-FDE is obtained from the standard diffusion equation by replacing the first-order time derivative by the Caputo fractional derivative and the second order space derivative by the symmetric fractional derivative. Firstly, a method of separating variables is used to express the analytical solution of the tss-fde in terms of the Mittag–Leffler function. Secondly, we propose two numerical methods to approximate the Caputo time fractional derivative, namely, the finite difference method and the Laplace transform method. The symmetric space fractional derivative is approximated using the matrix transform method. Finally, numerical results are presented to demonstrate the effectiveness of the numerical methods and to confirm the theoretical claims.

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    3 citations in Scopus
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    ID Code: 37946
    Item Type: Conference Paper
    Additional URLs:
    ISSN: 1445-8735
    Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > NUMERICAL AND COMPUTATIONAL MATHEMATICS (010300) > Numerical Solution of Differential and Integral Equations (010302)
    Divisions: Past > QUT Faculties & Divisions > Faculty of Science and Technology
    Past > Schools > Mathematical Sciences
    Copyright Owner: Copyright 2009 Australian Mathematical Society.
    Deposited On: 14 Oct 2010 14:21
    Last Modified: 01 Mar 2012 00:06

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