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A Fourier method for the fractional diffusion equation describing sub-diffusion

✍ Scribed by Chang-Ming Chen; F. Liu; I. Turner; V. Anh

Publisher: Elsevier Science
Year: 2007
Tongue: English
Weight: 224 KB
Volume: 227
Category: Article
ISSN: 0021-9991
DOI: 10.1016/j.jcp.2007.05.012

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✦ Synopsis

In this paper, a fractional partial differential equation (FPDE) describing sub-diffusion is considered. An implicit difference approximation scheme (IDAS) for solving a FPDE is presented. We propose a Fourier method for analyzing the stability and convergence of the IDAS, derive the global accuracy of the IDAS, and discuss the solvability. Finally, numerical examples are given to compare with the exact solution for the order of convergence, and simulate the fractional dynamical systems.

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