Error estimates for a fully discrete spectral scheme for a class of nonlinear, nonlocal dispersive wave equations

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Abstract

We analyze a fully discrete spectral method for the numerical solution of the initial- and periodic boundary-value problem for two nonlinear, nonlocal, dispersive wave equations, the Benjamin?Ono and the Intermediate Long Wave equations. The equations are discretized in space by the standard Fourier?Galerkin spectral method and in time by the explicit leap-frog scheme. For the resulting fully discrete, conditionally stable scheme we prove an L2-error bound of spectral accuracy in space and of second-order accuracy in time.
Original languageEnglish
Pages (from-to)95-107
Number of pages13
JournalApplied Numerical Mathematics
Volume37
Issue number1-2
DOIs
Publication statusPublished - Apr 2001

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