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Error analysis for spectral approximation of the Korteweg-de Vries equation. (English) Zbl 0647.65082

This paper presents the conservation and convergence properties of spectral Fourier methods for the numerical approximation of the KdV equation. It is proved that the collocation pseudospectral method enjoys the same convergence properties as the spectral Galerkin method which is less effective from the computational point of view. This paper really provides a precise mathematical answer to a question raised by several authors in the latest years.
Reviewer: P.K.Mahanti

MSC:

65Z05 Applications to the sciences
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35Q99 Partial differential equations of mathematical physics and other areas of application
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References:

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