留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

一维Burgers方程和KdV方程的广义有限谱方法

詹杰民 李毓湘

詹杰民, 李毓湘. 一维Burgers方程和KdV方程的广义有限谱方法[J]. 应用数学和力学, 2006, 27(12): 1431-1438.
引用本文: 詹杰民, 李毓湘. 一维Burgers方程和KdV方程的广义有限谱方法[J]. 应用数学和力学, 2006, 27(12): 1431-1438.
ZHAN Jie-min, LI Yok-sheng. Generalized Finite Spectral Method for 1D Burgers and KdV Equations[J]. Applied Mathematics and Mechanics, 2006, 27(12): 1431-1438.
Citation: ZHAN Jie-min, LI Yok-sheng. Generalized Finite Spectral Method for 1D Burgers and KdV Equations[J]. Applied Mathematics and Mechanics, 2006, 27(12): 1431-1438.

一维Burgers方程和KdV方程的广义有限谱方法

基金项目: 国家自然科学基金资助项目(10272118);教育部博士点专项基金资助项目(20020558013)
详细信息
    作者简介:

    詹杰民(1963- ),男,广东人,教授,博士,博士生导师(联系人.Tel:+86-20-8411130;Fax:+86-20-84113291;E-mail:stszjm@zsu.edu.cn).

  • 中图分类号: O351.2;O24

Generalized Finite Spectral Method for 1D Burgers and KdV Equations

  • 摘要: 给出了高精度的广义有限谱方法.为使方法在时间离散方面保持高精度,采用了Adams-Bashforth 预报格式和Adams-Moulton校正格式,为了避免由Korteweg-de Vries(KdV)方程的弥散项引起的数值振荡, 给出了两种数值稳定器.以Legendre多项式、Chebyshev多项式和Hermite多项式为基函数作为例子,给出的方法与具有分析解的Burgers方程的非线性对流扩散问题和KdV方程的单孤独波和双孤独波传播问题进行了比较,结果非常吻合.
  • [1] de Boussinesq J. Théorie des ondes et des remous qui se propagent le long d'un canal rectangulaire horizontal en communiquant au liquide continu dans ce canal des vitesses sensiblement pareilles de la surface au fond[J].J Math Pures et Appliquées,1872,17(2):55—108.
    [2] Korteweg D J, de Vries G. On the change of form of long waves advancing in a rectangular canal and on a new type of long sationary waves[J].Philosophical Magazine, 5th Series,1895,36:422—443.
    [3] Pego R L,Smereka P, Weinstein M I. Oscillatory instability of traveling waves for a KdV-Burgers equation[J].Physica D,1993,67(1/3):45—65. doi: 10.1016/0167-2789(93)90197-9
    [4] Ge H X, Dai S Q,Dong L Y,et al.Stabilization effect of traffic flow in an extended car-following model based on an intelligent transportation system application[J].Physical Review E,2004,70(6):Art.No.066134 Part 2.
    [5] Zhang C Y, Tan H L, Liu M R,et al.A lattice Boltzmann model and simulation of KdV-Burgers equation[J].Communications in Theoretical Physics,2004,42(2):281—284.
    [6] Kaya D.On the solution of a Korteweg-de Vries like equation by the decomposition method[J].International Journal of Computer Mathematics,1999,72(4):531—539. doi: 10.1080/00207169908804874
    [7] Kaya D. Solitary-wave solutions for compound KdV-type and compound KdV-Burgers-type equations with nonlinear terms of any order[J].Applied Mathematics and Computation,2004,152(3):709—720. doi: 10.1016/S0096-3003(03)00589-7
    [8] Patera A T. A spectral element method for fluid-dynamics -laminar-flow in a channel expansion[J].Journal of Computational Physics,1984,54(3):468—488. doi: 10.1016/0021-9991(84)90128-1
    [9] Ghaddar N K, Karniadakis G E, Patera A T. A conservative isoparametric spectral element method for forced convection: Application to fully developed flow in periodic geometries[J].Numer Heat Transfer,1986,9(3):277—300.
    [10] Giraldo F X. Strong and weak Lagrange-Galerkin spectral element methods for the shallow water equations[J].Computers and Mathematics With Applications,2003,45(1/3):97—121. doi: 10.1016/S0898-1221(03)80010-X
    [11] WANG Jian-ping.Non-periodic Fourier tansform and finite spectral method[A].In:Sixth Intere Symposium in CFD[C].Nevada:Lake Tahoe,1995,1339—1344.
    [12] WANG Jian-ping.Finite spectral method based on non-periodic Fourier transform[J].Computers and Fluids,1998,27(5/6):639—644. doi: 10.1016/S0045-7930(97)00056-X
    [13] 沈盂育,张增产,李海东. 高精度三点有限谱方法[J].清华大学学报(自然科学版),1997,37(8):52—54.
    [14] Su C H, Gardner C S.Derivation of the Korteweg-de Vries and Burgers equation[J].J Math Phys,1969,10(3):536—539. doi: 10.1063/1.1664873
    [15] Li Y S, Zhan J M.Boussinesq-type model with boundary-fitted coordinate system[J].Journal of Waterway Port Coastal and Ocean Engineering,ASCE,2001,127(3):152—160. doi: 10.1061/(ASCE)0733-950X(2001)127:3(152)
    [16] Beji S, Nadaoka K.A formal derivation and numerical modelling of the improved Boussinesq equations for varying depth[J].Ocean Engineering,1996,23(8):691—704. doi: 10.1016/0029-8018(96)84408-8
    [17] Press W H, Flannery B P, Teukolsky S A,et al.Numerical Recipes[M].New York:Cambridge University Press, 1989,569—572.
    [18] Wei G, Kirby J T.Time-dependent numerical code for extended Boussinesq equations[J].Journal of Waterway, Port, Coastal, and Ocean Engineering, ASCE,1995,121(5):251—260. doi: 10.1061/(ASCE)0733-950X(1995)121:5(251)
    [19] Dodd R K,Eilbeck J C,Gibbon J D,et al.Solitons and Nonlinear Wave Equations[M].New York :Academic Press, 1984.
    [20] Li P W. On the numerical study of the KdV equation by the semi-implicit and Leap-frog method[J].Computer Physics Communications,1995,88(2/3):121—127. doi: 10.1016/0010-4655(95)00060-S
  • 加载中
计量
  • 文章访问数:  3091
  • HTML全文浏览量:  157
  • PDF下载量:  782
  • 被引次数: 0
出版历程
  • 收稿日期:  2005-05-15
  • 修回日期:  2006-06-30
  • 刊出日期:  2006-12-15

目录

    /

    返回文章
    返回