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．
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关键词:
- Fourier谱方法 /
- 修改Fourier拟谱方法 /
- 广义KdV方程 /
- 误差估计
Abstract: A Fourier spectral method for the generalized Korteweg-de Vries equation with periodic boundary conditions is analyzed and corresponding optimal error estimate in L2-norm 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. -
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