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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.
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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

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