Hamiltonian boundary value methods applied to KdV-KdV systems

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成果类型：

期刊论文

作者：

Luo, Qian;Xiao, Aiguo;Luo, Xuqiong;Yan, Xiaoqiang

通讯作者：

Yan, XQ

作者机构：

[Luo, Qian; Xiao, Aiguo; Yan, Xiaoqiang] Xiangtan Univ, Sch Math & Computat Sci, Xiangtan 411105, Hunan, Peoples R China.

[Luo, Qian; Xiao, Aiguo; Yan, Xiaoqiang] Xiangtan Univ, Hunan Key Lab Computat & Simulat Sci & Engn, Xiangtan 411105, Hunan, Peoples R China.

[Luo, Qian; Xiao, Aiguo; Yan, Xiaoqiang] Minist Educ, Key Lab Intelligent Comp & Informat Proc, Xiangtan 411105, Hunan, Peoples R China.

[Luo, Xuqiong] Changsha Univ Sci & Technol, Sch Math & Stat, Changsha 410114, Peoples R China.

[Yan, Xiaoqiang] Xiangtan Univ, Natl Ctr Appl Math Hunan, Xiangtan 411105, Hunan, Peoples R China.

通讯机构：

[Yan, XQ ] X

Xiangtan Univ, Sch Math & Computat Sci, Xiangtan 411105, Hunan, Peoples R China.

Xiangtan Univ, Hunan Key Lab Computat & Simulat Sci & Engn, Xiangtan 411105, Hunan, Peoples R China.

语种：

英文

关键词：

KdV-KdV systems;Fourier-Galerkin methods;Hamiltonian boundary value methods;Blended iteration;Energy preservation

期刊：

Applied Numerical Mathematics

ISSN：

0168-9274

年：

2025

卷：

214

页码：

1-27

DOI：

10.1016/j.apnum.2025.02.006

基金类别：

NSFC [12201537,12071403,12101525]; Research Support Funding of Xiangtan University [22QDZ23,21QDZ16]; Youth Project of Hunan Provincial Natural Science Foundation of China [2024JJ6418]; Excellent Youth Project of Hunan Provincial Department of Education [24B0164]; Postgraduate Scientific Research Innovation Project of Hunan Province in China [CX20240590]; Postgraduate Scientific Research Innovation Project of Xiangtan University [XDCX2024Y140]

机构署名：

本校为其他机构

院系归属：

数学与统计学院

摘要：

In this paper, we propose a highly accurate scheme for two KdV systems of the Boussinesq type under periodic boundary conditions. The proposed scheme combines the Fourier-Galerkin method for spatial discretization with Hamiltonian boundary value methods for time integration, ensuring the conservation of discrete mass and energy. By expanding the system in Fourier series, the equations are firstly transformed into Hamiltonian form, preserving the original Hamiltonian structure. Applying the Fourier-Galerkin method for semi-discretization in space, we obtain a large-scale system of Hamiltonian o...

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Hamiltonian boundary value methods applied to KdV-KdV systems

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