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

Yang, Qianqian, Turner, Ian, & Liu, Fawang (2009) Analytical and numerical solutions for the time and space-symmetric fractional diffusion equation. Australian and New Zealand Industrial and Applied Mathematics Journal (ANZIAM), 50, 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 a Caputo fractional derivative, and the second order space derivative by a symmetric fractional derivative. First, a method of separating variables expresses the analytical solution of the TSS-FDE in terms of the Mittag--Leffler function. Second, we propose two numerical methods to approximate the Caputo time fractional derivative: the finite difference method; and the Laplace transform method. The symmetric space fractional derivative is approximated using the matrix transform method. Finally, numerical results demonstrate the effectiveness of the numerical methods and to confirm the theoretical claims.

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ID Code: 37852
Item Type: Journal Article
Keywords: time and space-symmetric fractional diffusion equation, TSS-FDE, Dirichlet conditions
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
Deposited On: 14 Oct 2010 10:21
Last Modified: 31 May 2011 09:13

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