A Novel High Order SpaceTime Spectral Method for the Time Fractional FokkerPlanck Equation
Zheng, Minling, Liu, Fawang, Turner, Ian, & Anh, Vo (2015) A Novel High Order SpaceTime Spectral Method for the Time Fractional FokkerPlanck Equation. SIAM Journal on Scientific Computing, 37(2), A701A724.

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Abstract
The fractional FokkerPlanck equation is an important physical model for simulating anomalous diffusions with external forces. Because of the nonlocal property of the fractional derivative an interesting problem is to explore high accuracy numerical methods for fractional differential equations. In this paper, a spacetime spectral method is presented for the numerical solution of the time fractional FokkerPlanck initialboundary value problem. The proposed method employs the Jacobi polynomials for the temporal discretization and Fourierlike basis functions for the spatial discretization. Due to the diagonalizable trait of the Fourierlike basis functions, this leads to a reduced representation of the inner product in the Galerkin analysis. We prove that the time fractional FokkerPlanck equation attains the same approximation order as the time fractional diffusion equation developed in [23] by using the present method. That indicates an exponential decay may be achieved if the exact solution is sufficiently smooth. Finally, some numerical results are given to demonstrate the high order accuracy and efficiency of the new numerical scheme. The results show that the errors of the numerical solutions obtained by the spacetime spectral method decay exponentially.
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ID Code:  82700 

Item Type:  Journal Article 
Refereed:  Yes 
DOI:  10.1137/140980545 
ISSN:  10957197 
Subjects:  Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > APPLIED MATHEMATICS (010200) > Dynamical Systems in Applications (010204) Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > NUMERICAL AND COMPUTATIONAL MATHEMATICS (010300) > Numerical Analysis (010301) 
Divisions:  Current > Research Centres > ARC Centre of Excellence for Mathematical & Statistical Frontiers (ACEMS) Current > Schools > School of Mathematical Sciences Current > QUT Faculties and Divisions > Science & Engineering Faculty 
Copyright Owner:  2015 Society for Industrial and Applied Mathematics 
Deposited On:  22 Mar 2015 22:32 
Last Modified:  10 Aug 2015 05:29 
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