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

Zhen-guo DENG;He-ping MA

doi:10.1007/s10483-009-0104-1

Applied Mathematics and Mechanics >

2009 , Vol. 30 >Issue 1: 29 - 38

DOI: https://doi.org/10.1007/s10483-009-0104-1

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

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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 date: 2008-03-05

Revised date: 2008-11-28

Online published: 2009-01-01

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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.

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Zhen-guo DENG;He-ping MA . Optimal error estimates for Fourier spectral approximation of the generalized KdV equation[J]. Applied Mathematics and Mechanics, 2009 , 30(1) : 29 -38 . DOI: 10.1007/s10483-009-0104-1

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