对称正则长波方程的高效紧致差分格式

高晶英; 何斯日古楞; 青梅; 额尔敦布和

doi:10.21656/1000-0887.440374

对称正则长波方程的高效紧致差分格式

doi: 10.21656/1000-0887.440374

呼和浩特民族学院数学与大数据学院，呼和浩特 010051

基金项目:

国家自然科学基金(12161034)

详细信息

作者简介:
高晶英(1989—)，男，副教授，博士(通讯作者. E-mail: minzugjy@email.imnc.edu.cn);何斯日古楞(1983—)，男，教授，博士，硕士生导师(E-mail: Cmml2005@163.com);青梅(1986—)，女，副教授，博士，硕士生导师(E-mail: bai.qingmei@163.com);额尔敦布和(1976—)，男，教授，博士，硕士生导师(E-mail: eerdunbuhe@163.com).

通讯作者:
高晶英(1989—)，男，副教授，博士(通讯作者. E-mail: minzugjy@email.imnc.edu.cn)

中图分类号: O241.82
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- 文章访问数: 22
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- PDF下载量: 5
- 被引次数: 0
出版历程
- 收稿日期: 2023-12-29
- 修回日期: 2024-07-16
- 网络出版日期: 2025-04-02
- 刊出日期: 2025-03-01

An Efficient Compact Difference Scheme for the Symmetric Regularized Long Wave Equation

School of Mathematics and Big Data, Hohhot Minzu College, Hohhot 010051, P.R.China

Funds:

The National Science Foundation of China(12161034)

摘要

摘要: 为了求出对称正则长波（symmetric regularized long wave, SRLW）方程的数值解，构造了一种新的高效紧致有限差分格式.采用经典的Crank-Nicolson(C-N)格式和外推技术对时间方向一阶导数进行离散化，使用四阶Padé 方法和逆紧致算子分别对空间方向一阶和二阶导数进行离散化，使得构造的格式具有线性、非耦合和紧致的特点，极大地提高了求解效率.此外，还对新格式进行了守恒律、先验估计、稳定性、收敛性分析，证明了其在时间上达到二阶、在空间上达到四阶收敛精度.最后，通过一个数值算例验证了理论的正确性和格式的高效性.
- 对称正则长波方程 /
- 有限差分 /
- 高效 /
- 紧致
Abstract: A new efficient and compact finite difference scheme was constructed to obtain numerical solutions of the symmetric regularized long wave equation. The classic Crank-Nicolson (C-N) scheme and the extrapolation technique were used for discretization of the 1st-order derivatives in the temporal direction, the 4th-order Padé method and the inverse compact operator were applied for discretization of the 1st-order and 2nd-order derivatives in the spatial direction, respectively. The constructed scheme has the linear, uncoupled, and compact features, greatly enhancing the computational efficiency. Additionally, analyses on conservation laws, a priori estimates, stability and convergence were conducted for the new scheme, to prove the 2nd-order temporal and the 4th-order spatial convergence accuracies. Finally, the theoretical correctness and efficiency of the scheme were verified through a numerical example.
- symmetric regularized long wave equation /
- finite difference /
- efficient /
- compact

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参考文献(22)

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