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广义KdV方程Fourier谱逼近的最优误差估计

邓镇国 马和平

邓镇国, 马和平. 广义KdV方程Fourier谱逼近的最优误差估计[J]. 应用数学和力学, 2009, 30(1): 30-39.
引用本文: 邓镇国, 马和平. 广义KdV方程Fourier谱逼近的最优误差估计[J]. 应用数学和力学, 2009, 30(1): 30-39.
DENG Zhen-guo, MA He-ping. Optimal Error Estimates for Fourier Spectral Approxiation of the Generalized KdV Equation[J]. Applied Mathematics and Mechanics, 2009, 30(1): 30-39.
Citation: DENG Zhen-guo, MA He-ping. Optimal Error Estimates for Fourier Spectral Approxiation of the Generalized KdV Equation[J]. Applied Mathematics and Mechanics, 2009, 30(1): 30-39.

广义KdV方程Fourier谱逼近的最优误差估计

基金项目: 国家自然科学基金资助项目(60874039);上海市重点学科建设资助项目(J50101)
详细信息
    作者简介:

    邓镇国(1978- ),男,广东人,博士(E-mail:zhgdeng@gmail.com);马和平,教授,博士,博士生导师(联系人.E-mail:hpma@shu.edu.cn).

  • 中图分类号: O241.82

Optimal Error Estimates for Fourier Spectral Approxiation of the Generalized KdV Equation

  • 摘要: 分析了一类带周期边界条件的广义KdV方程Fourier谱方法,得到了L2范数下最优误差估计,改进了由Maday和Quarteroni给出的结果.还提出了一种修改Fourier拟谱方法,并且证明它享有与Fourier谱方法同样的收敛性.
  • [1] Abe K,Inoue O.Fourier expansion solution of the KdV equation[J].J Computational Physics,1980, 34(2):202-210. doi: 10.1016/0021-9991(80)90105-9
    [2] Fornberg B,Whitham G B. A numerical and theoretical study of certain nonlinear phenomena[J].Phil Trans Roy Soc London Ser A,1978,289(1361):373-404. doi: 10.1098/rsta.1978.0064
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    [5] Maday Y,Quarteroni A. Error analysis for spectral approximation of the Korteweg-de Vries equation[J].RAIRO Modélisation Mathématique et Analyse Numérique,1988,22(3):499-529.
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    [7] Bjrkav[KG-*4]. ag M,Kalisch H. Exponential convergence of a spectral projection of the KdV equation[J].Physics Letters A,2007,365(4):278-283. doi: 10.1016/j.physleta.2006.12.085
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    [10] Ma M P,Sun W W. Optimal error estimates of the Legendre-Petrov-Galerkin method for the Korteweg-de Vries equation[J].SIAM J Numerical Analysis,2001,39(4):1380-1394. doi: 10.1137/S0036142900378327
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  • 被引次数: 0
出版历程
  • 收稿日期:  2008-03-05
  • 修回日期:  2008-11-28
  • 刊出日期:  2009-01-15

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