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Preconditioned iterative methods for space-time fractional advection-diffusion equations
Zhao Z.1; Jin X.-Q.2; Lin M.M.3
2016-08-15
Source PublicationJournal of Computational Physics
ISSN10902716 00219991
Volume319Pages:266-279
Abstract

In this paper, we propose practical numerical methods for solving a class of initial-boundary value problems of space-time fractional advection-diffusion equations. First, we propose an implicit method based on two-sided Grünwald formulae and discuss its stability and consistency. Then, we develop the preconditioned generalized minimal residual (preconditioned GMRES) method and preconditioned conjugate gradient normal residual (preconditioned CGNR) method with easily constructed preconditioners. Importantly, because resulting systems are Toeplitz-like, fast Fourier transform can be applied to significantly reduce the computational cost. We perform numerical experiments to demonstrate the efficiency of our preconditioners, even in cases with variable coefficients.

KeywordConjugate Gradient Normal Residual Method Fast Fourier Transform Fractional Diffusion Equations Generalized Minimal Residual Method Preconditioner Toeplitz Matrix
DOIhttps://doi.org/10.1016/j.jcp.2016.05.021
URLView the original
Indexed BySCI
WOS Research AreaComputer Science ; Physics
WOS SubjectComputer Science, Interdisciplinary Applications ; Physics, Mathematical
WOS IDWOS:000377044100014
PublisherACADEMIC PRESS INC ELSEVIER SCIENCE
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Citation statistics
Cited Times [WOS]:15   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
Affiliation1.Department of Mathematics, School of Science, Hangzhou Dianzi University, Hangzhou, China
2.Department of Mathematics, University of Macau, Macau, China
3.Department of Mathematics, National Chung Cheng University, Chia-Yi, Taiwan
Recommended Citation
GB/T 7714
Zhao Z.,Jin X.-Q.,Lin M.M.. Preconditioned iterative methods for space-time fractional advection-diffusion equations[J]. Journal of Computational Physics,2016,319:266-279.
APA Zhao Z.,Jin X.-Q.,&Lin M.M..(2016).Preconditioned iterative methods for space-time fractional advection-diffusion equations.Journal of Computational Physics,319,266-279.
MLA Zhao Z.,et al."Preconditioned iterative methods for space-time fractional advection-diffusion equations".Journal of Computational Physics 319(2016):266-279.
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