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Applied Mathematics and Mechanics (English Edition) ›› 2009, Vol. 30 ›› Issue (1): 29-38 .doi: https://doi.org/10.1007/s10483-009-0104-1

• Articles • Previous Articles     Next Articles

Optimal error estimates for Fourier spectral approximation of the generalized KdV equation

Zhen-guo DENG1,2;He-ping MA 1   

  1. 1. Department of Mathematics, Shanghai University,Shanghai 200444, P. R. China; 2. School of Mathematics and Information Science,Guangxi University, Nanning 530004, P. R. China
  • Received:2008-03-05 Revised:2008-11-28 Online:2009-01-01 Published:2009-01-01
  • Contact: He-ping MA

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Abstract: A Fourier spectral method for the generalized Korteweg-de Vries equation with periodic boundary conditions is analyzed, and a corresponding optimal error estimate in L2-norm is obtained. It improves the result presented by Maday and Quarteroni. A modified Fourier pseudospectral method is also presented, with the same convergence properties as the Fourier spectral method.

2010 MSC Number: 

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