Optimal error estimates of the Legendre-Petrov-Galerkin method for the Korteweg-De Vries equation

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)1380-1394
Journal / PublicationSIAM Journal on Numerical Analysis
Issue number4
Publication statusPublished - 2002


In this paper, the Legendre-Petrov-Galerkin method for the Korteweg-de Vries equation with nonperiodic boundary conditions is analyzed. The nonlinear term is computed with the Legendre spectral method and some pseudospectral methods, respectively. Optimal error estimates in L2-norm are obtained for both semidiscrete and fully discrete schemes. The method is also applicable to some (2m + 1)th-order differential equations.

Research Area(s)

  • Korteweg-de Vries equation, Legendre-Petrov-Galerkin, Pseudospectral