阻尼eKdV-Burgers方程的共形广义多辛Fourier拟谱算法

李骞; 王桂霞; 王一辰

doi:10.21656/1000-0887.450263

阻尼eKdV-Burgers方程的共形广义多辛Fourier拟谱算法

doi: 10.21656/1000-0887.450263

李骞¹,
王桂霞^1,2,3, ,,
王一辰¹

1. 内蒙古师范大学数学科学学院, 呼和浩特 010022;
2. 内蒙古自治区应用数学中心, 呼和浩特 010022;
3. 无穷维哈密顿系统及其算法应用教育部重点实验室, 呼和浩特 010022

基金项目:

国家自然科学基金(62161045)

内蒙古自治区自然科学基金(2023LHMS01007；2022JBQN074)

内蒙古自治区自然科学基金重点项目(2022ZD05)

详细信息

作者简介:
李骞(2000—), 女, 硕士生(E-mail: 3491240780@qq.com);王桂霞(1968—), 女, 教授, 博士(通讯作者. E-mail: nsdwgx@126.com).

通讯作者:
王桂霞(1968—), 女, 教授, 博士(通讯作者. E-mail: nsdwgx@126.com).

中图分类号: O241.82
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- 文章访问数: 11
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- 被引次数: 0
出版历程
- 收稿日期: 2024-09-29
- 修回日期: 2024-12-24
- 网络出版日期: 2025-12-05

A Conformal Generalized Multi-Symplectic Fourier Pseudo-Spectral Algorithm for Damping eKdV-Burgers Equations

LI Qian¹,
WANG Guixia^{1,2,3
, ,},
WANG Yichen¹

1. College of Mathematics Science, Inner Mongolia Normal University, Hohhot 010022, P.R.China;
2. Center for Applied Mathematics Science, Inner Mongolia, Hohhot 010022, P.R.China;
3. Laboratory of Infinite-Dimensional Hamiltonian System and Its Algorithm Application, Ministry of Education, Hohhot 010022, P.R.China

Funds:

The National Science Foundation of China(62161045)

摘要

摘要: 基于Hamilton共形广义多辛理论,研究一类阻尼eKdV-Burgers方程的共形广义多辛Fourier拟谱格式的保结构算法.首先,通过引入中间变量,将方程转化为满足局部守恒的共形广义多辛Hamilton系统,并利用Strang分裂方法,将其分裂为守恒子系统和耗散子系统.进一步,空间上利用Fourier拟谱方法,时间上利用隐中点方法,对该系统进行离散，得到共形广义多辛Fourier拟谱格式,在周期边界条件下,该格式满足全局共形质量守恒律和动量守恒律.数值实例表明该算法是有效的,能够保持系统质量和动量衰减特性.
- 耗散项 /
- 浅水效应 /
- eKdV-Burgers方程 /
- 共形广义多辛 /
- Fourier拟谱方法 /
- Strang分裂
Abstract: Based on the conformal generalized multi-symplectic theory for Hamiltonian systems, a class of conformal generalized multi-symplectic pseudo-spectral algorithms for damping eKdV-Burgers the equations were studied. Firstly, through introduction of intermediate variables, the equation was transformed into a conformal generalized multi-symplectic Hamiltonian system satisfying local conservation, and the Strang splitting method was used to split it into a conservative subsystem and a dissipative subsystem. Furthermore, the Fourier pseudo-spectral method was applied spatially and the hidden midpoint method applied temporally to discretize the system to obtain the conformal generalized multi-symplectic Fourier pseudo-spectral scheme, which meets the global conformal mass conservation law and the momentum conservation law under the periodic boundary conditions. Numerical examples show that, the algorithm is effective and can maintain the mass and momentum decay characteristics of the system.
- dissipative term /
- shallow water effect /
- eKdV-Burgers equation /
- conformal generalized multi-symplectic /
- Fourier pseudo-spectral method /
- Strang split

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参考文献(39)

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阻尼eKdV-Burgers方程的共形广义多辛Fourier拟谱算法

doi: 10.21656/1000-0887.450263

作者简介:
李骞(2000—), 女, 硕士生(E-mail: 3491240780@qq.com);王桂霞(1968—), 女, 教授, 博士(通讯作者. E-mail: nsdwgx@126.com).

通讯作者:
王桂霞(1968—), 女, 教授, 博士(通讯作者. E-mail: nsdwgx@126.com).

计量

A Conformal Generalized Multi-Symplectic Fourier Pseudo-Spectral Algorithm for Damping eKdV-Burgers Equations

计量

目录

留言板

阻尼eKdV-Burgers方程的共形广义多辛Fourier拟谱算法

doi: 10.21656/1000-0887.450263

作者简介: 李骞(2000—), 女, 硕士生(E-mail: 3491240780@qq.com);王桂霞(1968—), 女, 教授, 博士(通讯作者. E-mail: nsdwgx@126.com).

通讯作者: 王桂霞(1968—), 女, 教授, 博士(通讯作者. E-mail: nsdwgx@126.com).

计量

出版历程

A Conformal Generalized Multi-Symplectic Fourier Pseudo-Spectral Algorithm for Damping eKdV-Burgers Equations

计量

出版历程

目录

作者简介:
李骞(2000—), 女, 硕士生(E-mail: 3491240780@qq.com);王桂霞(1968—), 女, 教授, 博士(通讯作者. E-mail: nsdwgx@126.com).

通讯作者:
王桂霞(1968—), 女, 教授, 博士(通讯作者. E-mail: nsdwgx@126.com).