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.
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.
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Paulo Amorim 1; Mário Figueira 1
@article{CRMATH_2009__347_19-20_1135_0, author = {Paulo Amorim and M\'ario Figueira}, 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}, }
Paulo Amorim; Mário Figueira. Convergence of semi-discrete approximations of Benney equations. Comptes Rendus. Mathématique, Volume 347 (2009) no. 19-20, pp. 1135-1140. doi : 10.1016/j.crma.2009.08.002. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.08.002/
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