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Local energy‐ and momentum‐preserving schemes for Klein‐Gordon‐Schrödinger equations and convergence analysis
Author(s) -
Cai Jiaxiang,
Hong Jialin,
Wang Yushun
Publication year - 2017
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22145
Subject(s) - conservation law , momentum (technical analysis) , mathematics , energy–momentum relation , charge conservation , convergence (economics) , energy conservation , nonlinear system , partial differential equation , schrödinger equation , boundary (topology) , boundary value problem , numerical analysis , space (punctuation) , charge (physics) , mathematical analysis , classical mechanics , physics , quantum mechanics , computer science , ecology , finance , economics , biology , economic growth , operating system
In this article, we obtain local energy and momentum conservation laws for the Klein‐Gordon‐Schrödinger 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 ( τ 2 + h 2 ) . The theoretical properties are verified by numerical experiments. © 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1329–1351, 2017