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Optimal H 2 ‐error estimates of conservative compact difference scheme for the Zakharov equation in two‐space dimension
Author(s) -
Zhou Xuanxuan,
Wang Tingchun,
Ji Bingquan,
Zhang Luming
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5568
Subject(s) - mathematics , dimension (graph theory) , computation , fast fourier transform , nonlinear system , energy (signal processing) , scheme (mathematics) , mathematical analysis , space (punctuation) , fourier transform , algorithm , pure mathematics , statistics , linguistics , philosophy , physics , quantum mechanics
In this paper, a conservative compact difference scheme is proposed for the two‐dimensional nonlinear Zakharov equation with periodic boundary condition and initial condition. The proposed scheme not only conserve the mass and energy in the discrete level but also are efficient in practical experiments because the Fast Fourier transform (FFT) can be used to speed up the numerical computation. By using the standard energy method and induction argument, we can establish rigorously the unconditional and optimal H 2 ‐error estimates. Some numerical examples are provided to support our theoretical results and show the accuracy and efficiency of the new scheme.