Abstract

MUNOZ GRAJALES, Juan Carlos. Analysis of a Fourier-Galerkin numerical scheme for a 1D Benney-Luke-Paumond equation. Rev.colomb.mat. [online]. 2015, vol.49, n.2, pp.213-234. ISSN 0034-7426.  https://doi.org/10.15446/recolma.v49n2.60440.

Abstract We study convergence of the semidiscrete and fully discrete formulations of a Fourier-Galerkin numerical scheme to approximate solutions of a nonlinear Benney-Luke-Paumond equation that models long water waves with small amplitude propagating over a shallow channel with flat bottom. The accuracy of the numerical solver is checked using some exact solitary wave solutions. In order to apply the Fourier-spectral scheme in a non periodic setting, we approximate the initial value problem with x ∈ ℝ by the corresponding periodic Cauchy problem for x ∈ [0,L], with a large spatial period L.

Keywords : Solitary waves; water waves; spectral methods.

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