2019
DOI: 10.1002/mma.5568
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Optimal H2‐error estimates of conservative compact difference scheme for the Zakharov equation in two‐space dimension

Abstract: 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… Show more

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