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A linearized and second-order unconditionally convergent scheme for coupled time fractional Klein-Gordon-Schrödinger equation
Lyu P.1; Vong S.1
2018-11-01
Source PublicationNumerical Methods for Partial Differential Equations
ISSN10982426 0749159X
Volume34Issue:6Pages:2153-2179
Abstract

In this work, we study finite difference scheme for coupled time fractional Klein-Gordon-Schrödinger (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 (Formula presented.) norm with energy method. Numerical results are included to justify the theoretical statements.

KeywordFractional Klein-gordon-schrödinger Equations Linearized Scheme Second-order Convergent Unconditionally Convergent And Stable
DOIhttp://doi.org/10.1002/num.22282
URLView the original
Indexed BySCI
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000445333600013
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被引频次[WOS]:2   [WOS记录]     [WOS相关记录]
Document TypeJournal article
专题DEPARTMENT OF MATHEMATICS
Affiliation1.Universidade de Macau
2.Southwest University of Finance and EcoNomics
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Lyu P.,Vong S.. A linearized and second-order unconditionally convergent scheme for coupled time fractional Klein-Gordon-Schrödinger equation[J]. Numerical Methods for Partial Differential Equations,2018,34(6):2153-2179.
APA Lyu P.,&Vong S..(2018).A linearized and second-order unconditionally convergent scheme for coupled time fractional Klein-Gordon-Schrödinger equation.Numerical Methods for Partial Differential Equations,34(6),2153-2179.
MLA Lyu P.,et al."A linearized and second-order unconditionally convergent scheme for coupled time fractional Klein-Gordon-Schrödinger equation".Numerical Methods for Partial Differential Equations 34.6(2018):2153-2179.
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