A Fourier method for the fractional diffusion equation describing sub-diffusion |
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| Authors: | Chang-Ming Chen F Liu I Turner V Anh |
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| Institution: | aSchool of Mathematical Sciences, Xiamen University, Xiamen 361005, China;bSchool of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, Qld. 4001, Australia;cSchool of Mathematical Sciences, South China University of Technology, Guangzhou 510640, China |
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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. |
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| Keywords: | Fractional diffusion equation Sub-diffusion Implicit difference approximation Fourier method Stability Convergence |
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