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Fast numerical solution for fractional diffusion equations by exponential quadrature rule
Zhang,Lu1; Sun,Hai Wei1; Pang,Hong Kui2
2015-07-23
Source PublicationJournal of Computational Physics
ISSN10902716 00219991
Volume299Pages:130-143
Abstract

After spatial discretization to the fractional diffusion equation by the shifted Grünwald formula, it leads to a system of ordinary differential equations, where the resulting coefficient matrix possesses the Toeplitz-like structure. An exponential quadrature rule is employed to solve such a system of ordinary differential equations. The convergence by the proposed method is theoretically studied. In practical computation, the product of a Toeplitz-like matrix exponential and a vector is calculated by the shift-invert Arnoldi method. Meanwhile, the coefficient matrix satisfies a condition that guarantees the fast approximation by the shift-invert Arnoldi method. Numerical results are given to demonstrate the efficiency of the proposed method.

KeywordExponential Quadrature Rule Fractional Diffusion Equation Matrix Exponential Preconditioned Gmres Shift-invert Arnoldi Toeplitz-like Structure
DOI10.1016/j.jcp.2015.07.001
URLView the original
Indexed BySCIE
Language英語English
WOS Research AreaComputer Science ; Physics
WOS SubjectComputer Science, Interdisciplinary Applications ; Physics, Mathematical
WOS IDWOS:000360087400010
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Cited Times [WOS]:20   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionFaculty of Science and Technology
Personal research not belonging to the institution
Affiliation1.Department of Mathematics, University of Macau,Macao
2.School of Mathematics and Statistics, Jiangsu Normal University,Xuzhou, Jiangsu,221116,China
First Author AffilicationUniversity of Macau
Recommended Citation
GB/T 7714
Zhang,Lu,Sun,Hai Wei,Pang,Hong Kui. Fast numerical solution for fractional diffusion equations by exponential quadrature rule[J]. Journal of Computational Physics,2015,299:130-143.
APA Zhang,Lu,Sun,Hai Wei,&Pang,Hong Kui.(2015).Fast numerical solution for fractional diffusion equations by exponential quadrature rule.Journal of Computational Physics,299,130-143.
MLA Zhang,Lu,et al."Fast numerical solution for fractional diffusion equations by exponential quadrature rule".Journal of Computational Physics 299(2015):130-143.
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