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Conservative compact finite difference scheme for the N‐coupled nonlinear Klein–Gordon equations
Author(s) -
Ji Bingquan,
Zhang Luming,
Zhou Xuanxuan
Publication year - 2019
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.22338
Subject(s) - mathematics , nonlinear system , compact finite difference , convergence (economics) , a priori and a posteriori , energy (signal processing) , conservation law , klein–gordon equation , mathematical analysis , space (punctuation) , function (biology) , finite difference , finite difference method , order (exchange) , scheme (mathematics) , finite element method , physics , philosophy , statistics , linguistics , epistemology , finance , quantum mechanics , evolutionary biology , economics , biology , economic growth , thermodynamics
In this article, a compact finite difference method is developed for the periodic initial value problem of the N‐coupled nonlinear Klein–Gordon equations. The present scheme is proved to preserve the total energy in the discrete sense. Due to the difficulty in obtaining the priori estimate from the discrete energy conservation law, the cut‐off function technique is employed to prove the convergence, which shows the new scheme possesses second order accuracy in time and fourth order accuracy in space, respectively. Additionally, several numerical results are reported to confirm our theoretical analysis. Lastly, we apply the reliable method to simulate and study the collisions of solitary waves numerically.