Volume 40 Issue 5
May. 2023
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JOURNAL OF MECHANICAL ENGINEERING  > 2023  >  44(5): 583-594.
PAN Yueyue, YANG Xiaozhong. A New Class of Difference Schemes With Intrinsic Parallelism for the KdV-Burgers Equation[J]. JOURNAL OF MECHANICAL ENGINEERING, 2023, 44(5): 583-594. doi: 10.21656/1000-0887.430128
Citation: PAN Yueyue, YANG Xiaozhong. A New Class of Difference Schemes With Intrinsic Parallelism for the KdV-Burgers Equation[J]. JOURNAL OF MECHANICAL ENGINEERING, 2023, 44(5): 583-594. doi: 10.21656/1000-0887.430128
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A New Class of Difference Schemes With Intrinsic Parallelism for the KdV-Burgers Equation

doi: 10.21656/1000-0887.430128

  • 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)

  • Received Date: 11 Apr 2022
  • Rev Recd Date: 14 Jun 2022
  • Issue Publish Date: 31 May 2023
    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.

     

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  • [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))
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