[Convergence d'une approximation semi-discrète des équations de Benney]
Dans la première partie de cette Note, on étudie l'approximation numérique des équations de Benney dans le cas de résonance des ondes courtes et longues. On prouve la convergence d'un schéma aux différences finies semi-discret dans l'espace de l'énérgie. Dans la deuxième partie de cette Note, on condidère une version quasilinéaire des équations de Benney. On prouve la convergence d'un schéma du type Lax–Friedrichs semi-discret vers la solution d'entropie du problème.
In the first part of this Note we study the numerical approximation of Benney equations in the long wave-short wave resonance case. We prove the convergence of a finite-difference semi-discrete scheme in the energy space. In the second part of the Note we consider the semi-discretization of a quasilinear version of Benney equations. We prove the convergence of a finite-difference semi-discrete Lax–Friedrichs type scheme towards a weak entropy solution of the Cauchy problem.
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@article{CRMATH_2009__347_19-20_1135_0,
author = {Amorim, Paulo and Figueira, M\'ario},
title = {Convergence of semi-discrete approximations of {Benney} equations},
journal = {Comptes Rendus. Math\'ematique},
pages = {1135--1140},
publisher = {Elsevier},
volume = {347},
number = {19-20},
year = {2009},
doi = {10.1016/j.crma.2009.08.002},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2009.08.002/}
}
TY - JOUR AU - Amorim, Paulo AU - Figueira, Mário TI - Convergence of semi-discrete approximations of Benney equations JO - Comptes Rendus. Mathématique PY - 2009 SP - 1135 EP - 1140 VL - 347 IS - 19-20 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2009.08.002/ DO - 10.1016/j.crma.2009.08.002 LA - en ID - CRMATH_2009__347_19-20_1135_0 ER -
%0 Journal Article %A Amorim, Paulo %A Figueira, Mário %T Convergence of semi-discrete approximations of Benney equations %J Comptes Rendus. Mathématique %D 2009 %P 1135-1140 %V 347 %N 19-20 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2009.08.002/ %R 10.1016/j.crma.2009.08.002 %G en %F CRMATH_2009__347_19-20_1135_0
Amorim, Paulo; Figueira, Mário. Convergence of semi-discrete approximations of Benney equations. Comptes Rendus. Mathématique, Tome 347 (2009) no. 19-20, pp. 1135-1140. doi : 10.1016/j.crma.2009.08.002. http://www.numdam.org/articles/10.1016/j.crma.2009.08.002/
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