KdV-Burgers方程的一类新本性并行差分格式

潘悦悦; 杨晓忠

doi:10.21656/1000-0887.430128

KdV-Burgers方程的一类新本性并行差分格式

doi: 10.21656/1000-0887.430128

潘悦悦¹,
杨晓忠^2, ,

1. 华北电力大学控制与计算机工程学院, 北京 102206;
2. 华北电力大学数理学院, 北京 102206

基金项目:

国家自然科学基金项目(11371135)

详细信息

作者简介:
潘悦悦(1995—)，女，博士生(E-mail: panyueyue@ncepu.edu.cn); 杨晓忠(1965—)，男，教授，博士生导师(通讯作者. E-mail: yxiaozh@ncepu.edu.cn).

通讯作者:
杨晓忠(1965—)，男，教授，博士生导师(通讯作者. E-mail: yxiaozh@ncepu.edu.cn).

中图分类号: O241.8
计量
- 文章访问数: 44
- HTML全文浏览量: 25
- PDF下载量: 0
- 被引次数: 0
出版历程
- 收稿日期: 2022-04-11
- 修回日期: 2022-06-14
- 刊出日期: 2023-05-31

A New Class of Difference Schemes With Intrinsic Parallelism for the KdV-Burgers Equation

PAN Yueyue¹,
YANG Xiaozhong^{2
, ,}

1. School of Control and Computer Engineering, North China Electric Power University, Beijing 102206, P.R.China;
2. School of Mathematics and Physics, North China Electric Power University, Beijing 102206, P.R.China

Funds:

The National Natural Science Foundation of China(11371135)

摘要

摘要: KdV-Burgers方程作为湍流规范方程，具有深刻的物理背景，其快速数值解法具有重要的实际应用价值.针对KdV-Burgers方程，提出了一种新型的并行差分格式.基于交替分段技术，结合经典Crank-Nicolson(C-N)格式、显格式和隐格式，构造了混合交替分段Crank-Nicolson(MASC-N)差分格式.理论分析表明MASC-N格式是唯一可解、线性绝对稳定和二阶收敛的.数值试验表明， MASC-N格式比C-N格式有更高的精度和效率.与ASE-I和ASC-N差分格式相比，MASC-N并行差分格式有最好的性能.表明该文的MASC-N并行差分方法能有效地求解KdV-Burgers方程.
- KdV-Burgers方程 /
- MASC-N并行差分格式 /
- 线性绝对稳定性 /
- 收敛性 /
- 数值试验
Abstract: The KdV-Burgers equation as a standard equation for turbulent, has a profound physical background and its fast numerical methods are of great practical application value. A new class of parallel difference schemes were proposed for the KdV-Burgers equation. Based on the alternating segment technology, the mixed alternating segment Crank-Nicolson (MASC-N) difference scheme was constructed with the classic Crank-Nicolson (C-N) scheme, the explicit and implicit schemes. The theoretical analyses indicate that, the MASC-N scheme is uniquely solvable, linearly absolutely stable and 2nd-order convergent. Numerical experiments show that, the MASC-N scheme has higher precision and efficiency than the C-N scheme. Compared with the ASE-I and ASC-N difference schemes, the MASC-N parallel difference scheme has the best performance, and can effectively solve the KdV-Burgers equation.
- KdV-Burgers equation /
- MASC-N parallel difference scheme /
- linear absolute stability /
- convergence /
- numerical experiment

HTML全文

参考文献(30)

[1]	叶其孝, 李正元, 王明新, 等. 反应扩散方程引论[M].2版. 北京: 科学出版社, 2011.(YE Qixiao, LI Zhengyuan, WANG Mingxin, et al.Introduction to Reaction-Diffusion Equations.[M].2nd ed. Beijing: Science Press, 2011.(in Chinese))
[2]HUANG J H, ZOU X F. Travelling wave fronts in diffusive and cooperative Lotka-Volterra system with delays[J].Journal of Mathematical Analysis and Applications,2002,271: 455-466.
[3]WU J H, ZOU X F. Traveling wave fronts of reaction diffusion systems with delay[J].Journal of Dynamics and Differential Equations,2001,13: 651-687.
[4]LV G Y, WANG M X. Traveling wave front in diffusive and competitive Lotka-Volterra system with delays[J].Nonlinear Analysis: Real World Applications,2010,11(3): 1323-1329.
[5]GUO J S, WU C H. Traveling wave front for a two-component lattice dynamical system arising in competitionmodels[J].. Journal of Differential Equations,. 2012,252(8): 4357-4391.
[6]LI K, HUANG J H, LI X, et al. Traveling wave fronts in a delayed lattice competitive system[J].Applicable Analysis,. 2017,97(6): 982-999.
[7]张秋, 陈广生. 一类具有非线性发生率与时滞的非局部扩散SIR模型的临界波的存在性[J]. 应用数学和力学, 2019,40(7): 713-727.(ZHANG Qiu, CHEN Guangsheng. Existence of critical traveling waves for nonlocal dispersal SIR models with delay and nonlinear incidence[J].Applied Mathematics and Mechanics,2019,40(7): 713-727.(in Chinese))
[8]谷雨萌, 黄明迪. 一类时间周期的时滞竞争系统行波解的存在性[J]. 应用数学和力学, 2020,41(6): 658-668.(GU Yumeng, HUANG Mingdi. Existence of periodic traveling waves for time-periodic Lotka-Volterra competition systems with delay[J].Applied Mathematics and Mechanics,2020,41(6): 658-668.(in Chinese))
[9]BRAMSON M.Convergence of Solutions of the Kolmogorov Equation to Traveling Waves.[M]. Memoirs of the American Mathematical Society, 1983.
[10]KIRCHGSSNER K. On the nonlinear dynamics of travelling fronts[J].Journal of Differential Equations,1992,96(2): 256-278.
[11]TSAI J C, SNEYD J. Existence and stability of traveling waves in bufferedsystems[J].SIAM Journal on Mathematical Analysis,2005,66: 237-265.
[12]MA S W, ZHAO X Q. Global asymptotic stability of minimal fronts in monostable lattice equations[J].Discrete and Continuous Dynamical Systems,2008,21: 259-275.
[13]WANG Y, CAO X Y, MA Z H,et al. Global stability of noncritical traveling front solutions of Fisher-type equations with degenerate nonlinearity[J].Journal of Mathematical Physics,. 2021,62(5): 051506.
[14]ZHOU Y H, YAN Z M, JI S G. Global stability of traveling waves with non-monotonicity for population dynamicsmodel[J].Tokyo Journal of Mathematics,. 2021,44: 383-396.
[15]LIU C C, MEI M, YANG J Q. Global stability of traveling waves for nonlocal time-delayed degenerate diffusion equation[J].Journal of Differential Equations,2022,306: 60-100.
[16]SCHAAF K W. Asymptotic behavior and traveling wave solutions for parabolic functional differentialequations[J].Transactions of the American Mathematical Society,1987,302: 587-615.
[17]MEI M, SO J W H, LI M Y, et al. Asymptotic stability of traveling waves for the Nicholson’s blowflies equation with diffusion[J].Proceedings of the Royal Society of Edinburgh Section A: Mathematics,2004,134(3): 579-594.
[18]LIN C K, MEI M. On travellingwavefronts of the Nicholson’s blowflies equations with diffusion[J].Proceedings of the Royal Society of Edinburgh Section A: Mathematics,. 2010,140(1): 135-152.
[19]MEI M, LIN C K, LIN C T, et al. Traveling wavefronts for time-delayed reaction-diffusion equation,Ⅰ: local nonlinearity[J].Journal of Differential Equations,2009,247(2): 495-510.
[20]MEI M, LIN C K, LIN C T, et al. Traveling wavefronts for time-delayed reaction-diffusion equation, Ⅱ: nonlocal nonlinearity[J].Journal of Differential Equations,2009,247(2): 511-529.
[21]YU Z X, XU F, ZHANG W G. Stability of invasion traveling waves for a competition system with nonlocaldispersals[J].Applicable Analysis,. 2017,96(7): 1107-1125.
[22]ZHANG G B, DONG F D, LI W T. Uniqueness and stability of traveling waves for a three-species competition system with nonlocaldispersal[J].Discrete and Continuous Dynamical Systems(Series B),2019,24(4): 1511-1541.
[23]MA S, ZOU X F. Existence, uniqueness and stability of traveling waves in a discrete reaction-diffusionmonostable equation with delay[J].Journal of Differential Equations,2005,217(1): 54-87.
[24]GUO S J, ZIMMER J. Stability of travelingwavefronts in discrete reaction-diffusion equations with nonlocal delay effects[J].Nonlinearity,2015,28(2): 463-492.
[25]HSU C H, LIN J J, YANG T S. Stability for monostable wave fronts of delayed lattice differential equations[J].Journal of Dynamics and Differential Equations,2017,29: 323-342.
[26]YU Z X, HSU C H. Wave propagation and its stability for a class of discrete diffusion systems[J].Zeitschrift für Angewandte Mathematik und Physik,2020,71: 194.
[27]CHEN G S, WU S L, HSU C H. Stability of travelingwavefronts for a discrete diffusive competition system with three species[J].Journal of Mathematical Analysis and Applications,2019,474(2): 909-930.
[28]SU T, ZHANG G B. Stability of travelingwavefronts for a three-component Lotka-Volterra competition system on a lattice[J].Electronic Journal of Differential Equations,2018,57(2018): 1-16.
[29]HSU C H, LIN J J. Stability analysis of traveling wave solutions for lattice reaction-diffusion equations[J].Discrete and Continuous Dynamical Systems(Series B),2020,25(5): 1757-1774.
[30]朱福国. 格上时滞Lotka-Volterra合作系统的波前解[J]. 生物数学学报, 2012,27(1): 150-156.(ZHU Fuguo. Traveling wavefrons of delayed Lotka-Volterra system on lattice[J].Journal of Biomathematics,2012,27(1): 150-156.(in Chinese))

施引文献

资源附件(0)

访问统计

点击查看大图

计量

文章访问数: 44
HTML全文浏览量: 25
PDF下载量: 0
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

留言板

KdV-Burgers方程的一类新本性并行差分格式

doi: 10.21656/1000-0887.430128

作者简介:
潘悦悦(1995—)，女，博士生(E-mail: panyueyue@ncepu.edu.cn); 杨晓忠(1965—)，男，教授，博士生导师(通讯作者. E-mail: yxiaozh@ncepu.edu.cn).

通讯作者:
杨晓忠(1965—)，男，教授，博士生导师(通讯作者. E-mail: yxiaozh@ncepu.edu.cn).

计量

A New Class of Difference Schemes With Intrinsic Parallelism for the KdV-Burgers Equation

计量

目录

留言板

KdV-Burgers方程的一类新本性并行差分格式

doi: 10.21656/1000-0887.430128

作者简介: 潘悦悦(1995—)，女，博士生(E-mail: panyueyue@ncepu.edu.cn); 杨晓忠(1965—)，男，教授，博士生导师(通讯作者. E-mail: yxiaozh@ncepu.edu.cn).

通讯作者: 杨晓忠(1965—)，男，教授，博士生导师(通讯作者. E-mail: yxiaozh@ncepu.edu.cn).

计量

出版历程

A New Class of Difference Schemes With Intrinsic Parallelism for the KdV-Burgers Equation

计量

出版历程

目录

作者简介:
潘悦悦(1995—)，女，博士生(E-mail: panyueyue@ncepu.edu.cn); 杨晓忠(1965—)，男，教授，博士生导师(通讯作者. E-mail: yxiaozh@ncepu.edu.cn).

通讯作者:
杨晓忠(1965—)，男，教授，博士生导师(通讯作者. E-mail: yxiaozh@ncepu.edu.cn).