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A conservative compact difference scheme for the coupled Klein–Gordon–Schrödinger equation
Author(s) -
Sun Qihang,
Zhang Luming,
Wang Shanshan,
Hu Xiuling
Publication year - 2013
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.21770
Subject(s) - mathematics , a priori and a posteriori , norm (philosophy) , convergence (economics) , partial differential equation , klein–gordon equation , scheme (mathematics) , mathematical analysis , initial value problem , basis (linear algebra) , a priori estimate , geometry , quantum mechanics , law , physics , nonlinear system , philosophy , economics , economic growth , epistemology , political science
In this article, a conservative compact difference scheme is presented for the periodic initial‐value problem of Klein–Gordon–Schrödinger equation. On the basis of some inequalities about norms and the priori estimates, convergence of the difference solution is proved with order O ( h 4 +τ 2 ) in maximum norm. Numerical experiments demonstrate the accuracy and efficiency of the compact scheme. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013