Optimal H2-error estimates of conservative compact difference scheme for the Zakharov equation in two-space dimension

被引：4

作者：

Zhou, Xuanxuan ^{[1
]}

Wang, Tingchun ^{[2
]}

Ji, Bingquan ^{[1
]}

Zhang, Luming ^{[1
]}

机构：

[1] Nanjing Univ Aeronaut & Astronaut, Coll Sci, Nanjing 211106, Jiangsu, Peoples R China

[2] Nanjing Univ Informat Sci & Technol, Sch Math & Stat, Nanjing, Jiangsu, Peoples R China

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2019年 / 42卷 / 09期

基金：

中国国家自然科学基金;

关键词：

conservative compact scheme; FFT; stability; unconditional convergence; Zakharov equation; NONLINEAR SCHRODINGER-EQUATION; 4TH-ORDER COMPACT; NUMERICAL-METHODS; CONVERGENCE; EFFICIENT; ACCURACY; MODEL;

D O I：

10.1002/mma.5568

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：3088 / 3102

页数：15

共 33 条

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