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

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

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...

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Veröffentlicht in:Journal of computational physics 2007-12, Vol.227 (2), p.886-897
Hauptverfasser: Chen, Chang-Ming, Liu, F., Turner, I., Anh, V.
Format: Artikel
Sprache:eng
Schlagworte:
Computational techniques
Convergence
Exact sciences and technology
Fourier method
Fractional diffusion equation
Implicit difference approximation
Mathematical methods in physics
Physics
Stability
Sub-diffusion
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Zusammenfassung: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.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2007.05.012