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广义KdV方程Fourier谱逼近的最优误差估计 被引量：2

Optimal Error Estimates for Fourier Spectral Approxiation of the Generalized KdV Equation
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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. A Fourier spectral method for the generalized Korteweg-de Vries equation with periodic boundary conditions is analyzed and corresponding optimal error estimate in L2-nonn is obtained, which improves the one by Maday and Quarteroni. Also a modified Fourier pseudospectral method is presented and it is proven that it enjoys the same convergence properties as the Fourier spectral method.
作者 邓镇国 马和平
机构地区 上海大学数学系 广西大学数学与信息科学学院
出处 《应用数学和力学》 CSCD 北大核心 2009年第1期30-39,共10页 Applied Mathematics and Mechanics
基金 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)
关键词 FOURIER谱方法 修改Fourier拟谱方法 广义KDV方程 误差估计 Fourier spectral method modified Fourier pseudospectral method generalized Korteweg-de Vries equation error estimate
分类号 O241.82 [理学—计算数学]
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参考文献11

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同被引文献17

  • 1李保安,尤国伟,秦青.BBM方程的周期波解和孤立波解[J].河南科技大学学报（自然科学版）,2004,25(5):70-73. 被引量：7
  • 2李志斌.非线性数学物理方程的行波解[M].北京:科技出版社.2006.
  • 3Wazwaz A M. The tanh method for travelling wave solutions of nonlinear equations[J]. Appl Math Comput, 2004, 154(3) :713-723.
  • 4ZHANG Sheng, XIA Tie-cheng. A generalized new auxiliary equation method and its applications to nonlinear partial differential equations[J]. Phys Lett A, 2007, 363(5/6) :355-350.
  • 5Wazwaz A M. A sine-cosine method for handling nonlinear wave equations[ J]. Math Comput Modelling, 2004, 40 (5/6) : 499-508.
  • 6ZHANG Sheng. Application of Exp-function method for (3+1)-dimensional nonlinear evolution equations[Jl. Computers Mathematics with Applications, 2008, 56(5) : 1451-1456.
  • 7WANG Ming-liang, LI Xiang-zheng, ZHANG Jing-liang. The (G/G')-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics [J]. Phys Lett A, 2008 , 372(4):417-423.
  • 8Bekir A. Application of the (G/G')-expansion method for nonlinear evolution equations [J]. Phys Lett A, 2008, 372(19): 3400-3405.
  • 9ZHANG Jiao, WEI Xiao-li, LU Yong-jie. A generalized (G/G')-expansion method and its applications[J]. Phys Lett A, 2008, 372(20): 3653-3658.
  • 10ZHANG Sheng, TONG Jing-lin, WANG Wei. A generalized (G/G')-expansion method for the mKdV equation with variable coefficients [J]. Phys Lett A, 2008, 372 ( 13 ) : 2254-2257.

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应用数学和力学
2009年 第1期

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