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Stability of fully discrete schemes with interpolation-type fractional formulas for distributed-order subdiffusion equations
Liao, Hong-lin1; Lyu, Pin2; Vong, Seakweng2; Zhao, Ying1
2017-08
Source PublicationNUMERICAL ALGORITHMS
ISSN1017-1398
Volume75Issue:4Pages:845-878
Abstract

Two fully discrete methods are investigated for simulating the distributed-order sub-diffusion equation in Caputo's form. The fractional Caputo derivative is approximated by the Caputo's BDF1 (called L1 early) and BDF2 (or L1-2 when it was first introduced) approximations, which are constructed by piecewise linear and quadratic interpolating polynomials, respectively. It is shown that the first scheme, using the BDF1 formula, possesses the discrete minimum-maximum principle and nonnegativity preservation property such that it is stable and convergent in the maximum norm. The method using the BDF2 formula is shown to be stable and convergent in the discrete H (1) norm by using the discrete energy method. For problems of distributed order within a certain region, the method is also proven to preserve the discrete maximum principle and nonnegativity property. Extensive numerical experiments are provided to show the effectiveness of numerical schemes, and to examine the initial singularity of the solution. The applicability of our numerical algorithms to a problem with solution which lacks the smoothness near the initial time is examined by employing a class of power-type nonuniform meshes.

KeywordFractional Subdiffusion Equations Caputo Derivative Caputo's Bdf Formulas Minimum-maximum Principle Discrete Energy Method Stability And Convergence
DOIhttp://doi.org/10.1007/s11075-016-0223-7
URLView the original
Indexed BySCI
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000406214300001
PublisherSPRINGER
The Source to ArticleWOS
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Cited Times [WOS]:8   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
Affiliation1.Institute of SciencesPLA University of Science and TechnologyNanjingPeople’s Republic of China
2.Department of MathematicsUniversity of MacauMacauChina
Recommended Citation
GB/T 7714
Liao, Hong-lin,Lyu, Pin,Vong, Seakweng,et al. Stability of fully discrete schemes with interpolation-type fractional formulas for distributed-order subdiffusion equations[J]. NUMERICAL ALGORITHMS,2017,75(4):845-878.
APA Liao, Hong-lin,Lyu, Pin,Vong, Seakweng,&Zhao, Ying.(2017).Stability of fully discrete schemes with interpolation-type fractional formulas for distributed-order subdiffusion equations.NUMERICAL ALGORITHMS,75(4),845-878.
MLA Liao, Hong-lin,et al."Stability of fully discrete schemes with interpolation-type fractional formulas for distributed-order subdiffusion equations".NUMERICAL ALGORITHMS 75.4(2017):845-878.
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