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A linearized and second-order unconditionally convergent scheme for coupled time fractional Klein-Gordon-Schrodinger equation
Lyu, Pin1,2; Vong, Seakweng2
2018-11
Source PublicationNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
ISSN0749-159X
Volume34Issue:6Pages:2153-2179
Abstract

In this work, we study finite difference scheme for coupled time fractional Klein-Gordon-Schrodinger (KGS) equation. We proposed a linearized finite difference scheme to solve the coupled system, in which the fractional derivatives are approximated by some recently established discretization formulas. These formulas approximate the solution with second-order accuracy at points different form the grid points in time direction. Taking advantage of this property, our proposed linearized scheme evaluates the nonlinear terms on the previous time level. As a result, iterative method is dispensable. The coupled terms in the scheme bring difficulties in analysis. By carefully studying these effects, we proved that the proposed scheme is unconditionally convergent and stable in discrete L-2 norm with energy method. Numerical results are included to justify the theoretical statements.

KeywordFractional Klein-gordon-schrodinger Equations Linearized Scheme Second-order Convergent Unconditionally Convergent And Stable
DOI10.1002/num.22282
URLView the original
Indexed BySCIE
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000445333600013
PublisherWILEY
The Source to ArticleWOS
Fulltext Access
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Cited Times [WOS]:5   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
Corresponding AuthorVong, Seakweng
Affiliation1.Univ Macau, Dept Math, Macau, Peoples R China
2.Southwestern Univ Finance & Econ, Sch Econ Math, Chengdu, Sichuan, Peoples R China
First Author AffilicationUniversity of Macau
Recommended Citation
GB/T 7714
Lyu, Pin,Vong, Seakweng. A linearized and second-order unconditionally convergent scheme for coupled time fractional Klein-Gordon-Schrodinger equation[J]. NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS,2018,34(6):2153-2179.
APA Lyu, Pin,&Vong, Seakweng.(2018).A linearized and second-order unconditionally convergent scheme for coupled time fractional Klein-Gordon-Schrodinger equation.NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS,34(6),2153-2179.
MLA Lyu, Pin,et al."A linearized and second-order unconditionally convergent scheme for coupled time fractional Klein-Gordon-Schrodinger equation".NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS 34.6(2018):2153-2179.
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