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 16 条

[1] A conservative compact difference scheme for the Zakharov equations in one space dimension
Zhou, Xuanxuan
Zhang, Luming
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2018, 95 (02) : 279 - 302
[2] Unconditional and optimal H2-error estimates of two linear and conservative finite difference schemes for the Klein-Gordon-Schrodinger equation in high dimensions
Wang, Tingchun
Zhao, Xiaofei
Jiang, Jiaping
ADVANCES IN COMPUTATIONAL MATHEMATICS, 2018, 44 (02) : 477 - 503
[3] Unconditional and optimal H2-error estimates of two linear and conservative finite difference schemes for the Klein-Gordon-Schrödinger equation in high dimensions
Tingchun Wang
Xiaofei Zhao
Jiaping Jiang
Advances in Computational Mathematics, 2018, 44 : 477 - 503
[4] Uniform error bound of a conservative fourth-order compact finite difference scheme for the Zakharov system in the subsonic regime
Zhang, Teng
Wang, Tingchun
ADVANCES IN COMPUTATIONAL MATHEMATICS, 2022, 48 (04)
[5] A conservative difference scheme with optimal pointwise error estimates for two-dimensional space fractional nonlinear Schrodinger equations
Hu, Hongling
Jin, Xianlin
He, Dongdong
Pan, Kejia
Zhang, Qifeng
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2022, 38 (01) : 4 - 32
[6] Pointwise error estimates of compact difference scheme for mixed-type time-fractional Burgers? equation
Peng, Xiangyi
Xu, Da
Qiu, Wenlin
MATHEMATICS AND COMPUTERS IN SIMULATION, 2023, 208 : 702 - 726
[7] Maximum norm error estimates of fourth-order compact difference scheme for the nonlinear Schrodinger equation involving a quintic term
Hu, Hanqing
Hu, Hanzhang
JOURNAL OF INEQUALITIES AND APPLICATIONS, 2018,
[8] Optimal Point-Wise Error Estimate of a Compact Difference Scheme for the Coupled Gross-Pitaevskii Equations in One Dimension
Wang, Tingchun
JOURNAL OF SCIENTIFIC COMPUTING, 2014, 59 (01) : 158 - 186
[9] Optimal l∞ error estimates of the conservative scheme for two-dimensional Schrodinger equations with wave operator
Cheng, Xiujun
Yan, Xiaoqiang
Qin, Hongyu
Wang, Huiru
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2021, 100 : 74 - 82
[10] A FOURTH-ORDER COMPACT AND CONSERVATIVE DIFFERENCE SCHEME FOR THE GENERALIZED ROSENAU-KORTEWEG DE VRIES EQUATION IN TWO DIMENSIONS
Wang, Jue
Zeng, Qingnan
JOURNAL OF COMPUTATIONAL MATHEMATICS, 2019, 37 (04) : 541 - 555

← 1 2 →