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Preconditioned iterative methods for fractional diffusion equation
Lin F.-R.1; Yang S.-W.1; Jin X.-Q.2
Source PublicationJournal of Computational Physics

In this paper, we are concerned with numerical methods for the solution of initial-boundary value problems of anomalous diffusion equations of order α. ∈. (1, 2). The classical Crank-Nicholson method is used to discretize the fractional diffusion equation and then the spatial extrapolation is used to obtain temporally and spatially second-order accurate numerical estimates. Two preconditioned iterative methods, namely, the preconditioned generalized minimal residual (preconditioned GMRES) method and the preconditioned conjugate gradient for normal residual (preconditioned CGNR) method, are proposed to solve relevant linear systems. Numerical experiments are given to illustrate the efficiency of the methods. 

KeywordFft Fractional Diffusion Equation Preconditioned Cgnr Method Preconditioned Gmres Method Toeplitz Matrix
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Indexed BySCI
WOS Research AreaComputer Science ; Physics
WOS SubjectComputer Science, Interdisciplinary Applications ; Physics, Mathematical
WOS IDWOS:000326596600007
The Source to ArticleScopus
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Cited Times [WOS]:56   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
Corresponding AuthorJin X.-Q.
Affiliation1.Department of Mathematics, Shantou University, Shantou, Guangdong 515063, China
2.Department of Mathematics, University of Macau, Macao, China
Corresponding Author AffilicationUniversity of Macau
Recommended Citation
GB/T 7714
Lin F.-R.,Yang S.-W.,Jin X.-Q.. Preconditioned iterative methods for fractional diffusion equation[J]. Journal of Computational Physics,2013,256:109.
APA Lin F.-R.,Yang S.-W.,&Jin X.-Q..(2013).Preconditioned iterative methods for fractional diffusion equation.Journal of Computational Physics,256,109.
MLA Lin F.-R.,et al."Preconditioned iterative methods for fractional diffusion equation".Journal of Computational Physics 256(2013):109.
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