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

Authors:
Chang-Ming Chen;F. Liu;I. Turner;V. Anh
Affiliations:
School of Mathematical Sciences, Xiamen University, Xiamen 361005, China;School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, Qld. 4001, Australia and School of Mathematical Sciences, South China University of Technology, Guangz ...;School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, Qld. 4001, Australia;School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, Qld. 4001, Australia
Venue:
Journal of Computational Physics
Year:
2007

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Abstract

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.