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

DOI10.1007/s10483-009-0104-1zbMath1187.65106OpenAlexW1487293542MaRDI QIDQ1016158

Zhen-Guo Deng, He-Ping Ma

Publication date: 4 May 2009

Published in: Applied Mathematics and Mechanics. (English Edition) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10483-009-0104-1

zbMATH Keywords

convergenceerror estimategeneralized Korteweg-de Vries equationFourier spectral methodmodified Fourier pseudospectral method

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)

Related Items (2)

A new auxiliary equation method for finding travelling wave solutions to KdV equation ⋮ Numerical method satisfying the first two conservation laws for the Korteweg-de Vries equation

Cites Work

• Exponential convergence of a spectral projection of the KdV equation
• The Fourier pseudospectral method with a restrain operator for the Korteweg-de Vries equation
• Fourier expansion solution of the Korteweg-de Vries equation
• Rapid convergence of a Galerkin projection of the KdV equation
• Fourier Methods with Extended Stability Intervals for the Korteweg–de Vries Equation
• Error analysis for spectral approximation of the Korteweg-de Vries equation
• Stability of the Fourier Method
• A numerical and theoretical study of certain nonlinear wave phenomena
• Optimal Error Estimates of the Legendre--Petrov--Galerkin Method for the Korteweg--de Vries Equation

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