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Local energy- and momentum-preserving schemes for Klein-Gordon-Schrodinger equations and convergence analysis
Cai, Jiaxiang1,2; Hong, Jialin3; Wang, Yushun2
2017-07-01
Source PublicationNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
ISSN0749-159X
Volume33Issue:4Pages:1329-1351
AbstractIn this article, we obtain local energy and momentum conservation laws for the Klein-Gordon-Schrodinger equations, which are independent of the boundary condition and more essential than the global conservation laws. Based on the rule that the numerical methods should preserve the intrinsic properties as much as possible, we propose local energy- and momentum-preserving schemes for the equations. The merit of the proposed schemes is that the local energy/momentum conservation law is conserved exactly in any time-space region. With suitable boundary conditions, the schemes will be charge- and energy-/momentum-preserving. Nonlinear analysis shows LEP schemes are unconditionally stable and the numerical solutions converge to the exact solutions with order O(2+h2). The theoretical properties are verified by numerical experiments. (c) 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1329-1351, 2017
Keywordconservation law convergence analysis Klein-Gordon-Schrodinger equations local structure structure-preserving algorithm
DOI10.1002/num.22145
Language英语
Funding ProjectNational Natural Science Foundation of China[11201169] ; National Natural Science Foundation of China[11271195] ; National Natural Science Foundation of China[41231173] ; Jiangsu Key Laboratory for Numerical Simulation of Large Scale Complex Systems[201606]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000400172500015
PublisherWILEY
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/26103
Collection计算数学与科学工程计算研究所
Corresponding AuthorCai, Jiaxiang
Affiliation1.Huaiyin Normal Univ, Sch Math Sci, Huaian 223300, Jiangsu, Peoples R China
2.Nanjing Normal Univ, Sch Math Sci, Jiangsu Key Lab NSLSCS, Nanjing 210046, Jiangsu, Peoples R China
3.Chinese Acad Sci, State Key Lab Sci & Engn Comp, Inst Computat Math & Sci Engn Comp, AMSS, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Cai, Jiaxiang,Hong, Jialin,Wang, Yushun. Local energy- and momentum-preserving schemes for Klein-Gordon-Schrodinger equations and convergence analysis[J]. NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS,2017,33(4):1329-1351.
APA Cai, Jiaxiang,Hong, Jialin,&Wang, Yushun.(2017).Local energy- and momentum-preserving schemes for Klein-Gordon-Schrodinger equations and convergence analysis.NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS,33(4),1329-1351.
MLA Cai, Jiaxiang,et al."Local energy- and momentum-preserving schemes for Klein-Gordon-Schrodinger equations and convergence analysis".NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS 33.4(2017):1329-1351.
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