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High order finite difference method for time-space fractional differential equations with Caputo and Riemann-Liouville derivatives
Vong S.; Lyu P.; Chen X.; Lei S.-L.
2016
Source PublicationNumerical Algorithms
ISSN10171398
Volume72Issue:1Pages:195
Abstract

We consider high order finite difference methods for two-dimensional fractional differential equations with temporal Caputo and spatial Riemann-Liouville derivatives in this paper. We propose a scheme and show that it converges with second order in time and fourth order in space. The accuracy of our proposed method can be improved by Richardson extrapolation. Approximate solution is obtained by the generalized minimal residual (GMRES) method. A preconditioner is proposed to improve the efficiency for the implementation of the GMRES method. © 2015, Springer Science+Business Media New York.

KeywordDiscrete Energy Method High Order Difference Scheme Preconditioned Gmres Method Two-dimensional Fractional Differential Equation
DOI10.1007/s11075-015-0041-3
URLView the original
Indexed BySCIE
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000374842300011
The Source to ArticleScopus
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Cited Times [WOS]:50   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
Corresponding AuthorVong S.
AffiliationUniv Macau, Dept Math, Macau, Peoples R China
First Author AffilicationUniversity of Macau
Corresponding Author AffilicationUniversity of Macau
Recommended Citation
GB/T 7714
Vong S.,Lyu P.,Chen X.,et al. High order finite difference method for time-space fractional differential equations with Caputo and Riemann-Liouville derivatives[J]. Numerical Algorithms,2016,72(1):195.
APA Vong S.,Lyu P.,Chen X.,&Lei S.-L..(2016).High order finite difference method for time-space fractional differential equations with Caputo and Riemann-Liouville derivatives.Numerical Algorithms,72(1),195.
MLA Vong S.,et al."High order finite difference method for time-space fractional differential equations with Caputo and Riemann-Liouville derivatives".Numerical Algorithms 72.1(2016):195.
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