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A SPATIALLY SIXTH-ORDER HYBRID L1-CCD METHOD FOR SOLVING TIME FRACTIONAL SCHRÖDINGER EQUATIONS
Zhang, C. H.; Jin, J. W.; Sun, H. W.; Sheng, Q.
2021-03-01
Source PublicationAPPLICATIONS OF MATHEMATICS
ISSN1572-9109
Pages213-232
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 − in time, where 0 < < 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.

KeywordNonlinear Time Fractional Schrödinger Equations L1 Formula Hybrid Compact Difference Method Linearization Unconditional Stability
Language英語English
The Source to ArticlePB_Publication
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
Corresponding AuthorSun, H. W.
Recommended Citation
GB/T 7714
Zhang, C. H.,Jin, J. W.,Sun, H. W.,et al. A SPATIALLY SIXTH-ORDER HYBRID L1-CCD METHOD FOR SOLVING TIME FRACTIONAL SCHRÖDINGER EQUATIONS[J]. APPLICATIONS OF MATHEMATICS,2021:213-232.
APA Zhang, C. H.,Jin, J. W.,Sun, H. W.,&Sheng, Q..(2021).A SPATIALLY SIXTH-ORDER HYBRID L1-CCD METHOD FOR SOLVING TIME FRACTIONAL SCHRÖDINGER EQUATIONS.APPLICATIONS OF MATHEMATICS,213-232.
MLA Zhang, C. H.,et al."A SPATIALLY SIXTH-ORDER HYBRID L1-CCD METHOD FOR SOLVING TIME FRACTIONAL SCHRÖDINGER EQUATIONS".APPLICATIONS OF MATHEMATICS (2021):213-232.
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