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

DENG Zhen-guo; MA He-ping

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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.

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.

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

DENG Zhen-guo^1,2,
MA He-ping¹

1.
Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China;

Received Date: 2008-03-05
Rev Recd Date: 2008-11-28
Publish Date: 2009-01-15

Abstract

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.
- Fourier spectral method,
- modified Fourier pseudospectral method,
- generalized Korteweg-de Vries equation,
- error estimate

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References(11)

References

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