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
计量
- 文章访问数: 18
- HTML全文浏览量: 4
- PDF下载量: 4
- 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

HTML全文

参考文献(22)

SEYLER C E, FENSTERMACHER D L. A symmetric regularized-long-wave equation[J]. Physics of Fluids,1984,27(1): 4-7.

[2]PEREGRINE D H. Calculations of the development of an undular bore[J]. Journal of Fluid Mechanics,1966,25(2): 321-330.

[3]WANG B, SUN T, LIANG D. The conservative and fourth-order compact finite difference schemes for regularized long wave equation[J]. Journal of Computational and Applied Mathematics,2019,356: 98-117.

[4]潘悦悦, 杨晓忠. KdV-Burgers方程的一类新本性并行差分格式[J]. 应用数学和力学, 2023,44(5): 583-594.(PAN Yueyue, YANG Xiaozhong. A new class of difference schemes with intrinsic parallelism for the KdV-Burgers equation[J]. Applied Mathematics and Mechanics,2023,44(5): 583-594.(in Chinese))

[5]GUO B L. The spectral method for symmetric regularized wave equations[J]. Journal of Computational Mathematics,1987,5(4): 297-306.

[6]郑家栋, 张汝芬, 郭本瑜. SRLW方程的Fourier拟谱方法[J]. 应用数学和力学, 1989,10(9): 843-852. (ZHENG Jiadong, ZHANG Rufen, GUO Benyu. The Fourier pseudo-spectral method for the SRLW equation[J]. Applied Mathematics and Mechanics,1989,10(9): 843-852. (in Chinese))

[7]尚亚东, 郭柏灵. 多维广义SRLW方程的Chebyshev拟谱方法分析[J]. 应用数学和力学, 2003,24(10): 1168-1183. (SHANG Yadong, GUO Boling. Analysis of Chebyshev pseudospectral method for multi-dimensional generalized SRLW equations[J]. Applied Mathematics and Mechanics,2003,24(10): 1168-1183. (in Chinese))

[8]FANG S M, GUO B L, QIU H. The existence of global attractors for a system of multi-dimensional symmetric regularized wave equations[J]. Communications in Nonlinear Science and Numerical Simulation,2009,14(1): 61-68.

[9]魏剑英，葛永斌. 一种求解三维非稳态对流扩散反应方程的高精度有限差分格式[J]. 应用数学和力学, 2022,43(2): 187-197.(WEI Jianying, GE Yongbin. A high-order finite difference scheme for 3D unsteady convection diffusion reaction equations[J]. Applied Mathematics and Mechanics,2022,43(2): 187-197.(in Chinese))

[10]WANG T, ZHANG L, CHEN F. Conservative schemes for the symmetric regularized long wave equations[J]. Applied Mathematics and Computation,2007,190(2): 1063-1080.

[11]王强, 何斯日古楞. 对称正则长波方程的两层差分方法[J]. 内蒙古大学学报(自然科学版), 2016,47(6): 568-572.(WANG Qiang, HE Siriguleng. Two-step difference method for the symmetric regularized long wave equation[J]. Journal of Inner Mongolia University (Natural Science Edition), 2016,47(6): 568-572. (in Chinese))

[12]柏琰, 张鲁明. 对称正则长波方程的一个新的守恒差分格式[J]. 应用数学, 2009,22(1): 130-136.(BAI Yan, ZHANG Luming. A new conservative finite difference scheme for symmetric regularized long wave equations[J]. Mathematica Applicata,2009,22(1): 130-136. (in Chinese))

[13]YIMNET S, WONGSAIJAI B, ROJSIRAPHISAL T, et al. Numerical implementation for solving the symmetric regularized long wave equation[J]. Applied Mathematics and Computation,2016,273: 809-825.

[14]NIE T. A decoupled and conservative difference scheme with fourth-order accuracy for the symmetric regularized long wave equations[J]. Applied Mathematics and Computation,2013,219(17): 9461-9468.

[15]HU J, ZHENG K, ZHENG M. Numerical simulation and convergence analysis of a high-order conservative difference scheme for SRLW equation[J]. Applied Mathematical Modelling,2014,38(23): 5573-5581.

[16]KERDBOON J, YIMNET S, WONGSAIJAI B, et al. Convergence analysis of the higher-order global mass-preserving numerical method for the symmetric regularized long-wave equation[J]. International Journal of Computer Mathematics,2021,98(5): 869-902.

[17]HE Y, WANG X, CHENG H, et al. Numerical analysis of a high-order accurate compact finite difference scheme for the SRLW equation[J]. Applied Mathematics and Computation,2022,418: 126837.

[18]LI S. Numerical study of a conservative weighted compact difference scheme for the symmetric regularized long wave equations[J]. Numerical Methods for Partial Differential Equations,2019,35(1): 60-83.

[19]HE Y Y, WANG X F, ZHONG R H. A new linearized fourth-order conservative compact difference scheme for the SRLW equations[J]. Advances in Computational Mathematics,2022,48: 27.

[21]GAO J Y, HE S, BAI Q M, et al. A time two-mesh finite difference numerical scheme for the symmetric regularized long wave equation[J]. Fractal and Fractional,2023,7(6): 487.

YANG X J, ZHANG L, GE Y B. High-order compact finite difference schemes for solving the regularized long-wave equation[J]. Applied Numerical Mathematics,2023,185: 165-187.

[22]GAO J Y, BAI Q M, HE S, et al. New two-level time-mesh difference scheme for the symmetric regularized long wave equation[J]. Axioms,2023,12(11): 1057.

施引文献

资源附件(0)

访问统计