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A spatially sixth-order hybrid L1-CCD method for solving time fractional Schrödinger equations
Zhang,Chun Hua1; Jin,Jun Wei2; Sun,Hai Wei1; Sheng,Qin3
2021-04
Source PublicationApplications of Mathematics
ISSN0862-7940
Volume66Issue:2Pages:213–232
Abstract

We consider highly accurate schemes for nonlinear time fractional Schrödinger equations (NTFSEs). While an L1 strategy is employed for approximating the Caputo fractional derivative in the temporal direction, compact CCD finite difference approaches are incorporated in the space. A highly effective hybrid L1-CCD method is implemented successfully. The accuracy of this linearized scheme is order six in space, and order 2 — γ in time, where 0 < γ < 1 is the order of the Caputo fractional derivative involved. It is proved rigorously that the hybrid numerical method accomplished is unconditionally stable in the Fourier sense. Numerical experiments are carried out with typical testing problems to validate the effectiveness of the new algorithms.

Keyword65m06 65m20 65m60 Hybrid Compact Difference Method L1 Formula Linearization Nonlinear Time Fractional Schrödinger Equations Unconditional Stability
DOI10.21136/AM.2020.0339-19
URLView the original
Indexed BySCIE
Language英語English
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000605906800001
PublisherACAD SCIENCES CZECH REPUBLIC, INST MATHEMATICSZITNA 25, PRAHA 1 115 67, CZECH REPUBLIC
Scopus ID2-s2.0-85098862172
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Cited Times [WOS]:1   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
Corresponding AuthorJin,Jun Wei; Sun,Hai Wei; Sheng,Qin
Affiliation1.Department of Mathematics,University of Macau,Taipa, Macau,Avenida da Universidade,China
2.Key Laboratory of Grain Information Processing and Control,Ministry of Education of China,and College of Information Science and Engineering,Henan University of Technology,Zhengzhou,450001,China
3.Department of Mathematics and Center for Astrophysics,Space Physics and Engineering Research,Baylor University,Waco,76798-7328,United States
First Author AffilicationUniversity of Macau
Corresponding Author AffilicationUniversity of Macau
Recommended Citation
GB/T 7714
Zhang,Chun Hua,Jin,Jun Wei,Sun,Hai Wei,et al. A spatially sixth-order hybrid L1-CCD method for solving time fractional Schrödinger equations[J]. Applications of Mathematics,2021,66(2):213–232.
APA Zhang,Chun Hua,Jin,Jun Wei,Sun,Hai Wei,&Sheng,Qin.(2021).A spatially sixth-order hybrid L1-CCD method for solving time fractional Schrödinger equations.Applications of Mathematics,66(2),213–232.
MLA Zhang,Chun Hua,et al."A spatially sixth-order hybrid L1-CCD method for solving time fractional Schrödinger equations".Applications of Mathematics 66.2(2021):213–232.
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