NDLI: A Space-Time Spectral Method for the Time Fractional Diffusion Equation

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Li, Xianjuan Xu, Chuanju
Copyright Year	2009
Abstract	In this paper, we consider the numerical solution of the time fractional diffusion equation. Essentially, the time fractional diffusion equation differs from the standard diffusion equation in the time derivative term. In the former case, the first-order time derivative is replaced by a fractional derivative, making the problem global in time. We propose a spectral method in both temporal and spatial discretizations for this equation. The convergence of the method is proven by providing a priori error estimate. Numerical tests are carried out to confirm the theoretical results. Thanks to the spectral accuracy in both space and time of the proposed method, the storage requirement due to the global time dependence can be considerably relaxed, and therefore calculation of the long-time solution becomes possible.
Starting Page	2108
Ending Page	2131
Page Count	24
File Format	PDF
ISSN	00361429
DOI	10.1137/080718942
e-ISSN	10957170
Issue Number	3
Volume Number	47
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2009-06-10
Access Restriction	Subscribed
Subject Keyword	error estimate Stability and convergence of numerical methods time fractional diffusion equation Spectral, collocation and related methods Initial value problems for pseudodifferential operators space-time spectral method
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Numerical Analysis Computational Mathematics

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