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Comptes Rendus Mathématique
Volume 347, n° 19-20
pages 1135-1140 (octobre 2009)
Doi : 10.1016/j.crma.2009.08.002
Received : 17 June 2009 ;  accepted : 24 August 2009
Convergence of semi-discrete approximations of Benney equations
Convergence d’une approximation semi-discrète des équations de Benney
 

Paulo Amorim , Mário Figueira
Centro de Matemática e Aplicações Fundamentais, Universidade de Lisboa, Av. Prof. Gama Pinto 2, 1649-003 Lisboa, Portugal 

Abstract

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. To cite this article: P. Amorim, M. Figueira, C. R. Acad. Sci. Paris, Ser. I 347 (2009).

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Résumé

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. Pour citer cet article : P. Amorim, M. Figueira, C. R. Acad. Sci. Paris, Ser. I 347 (2009).

The full text of this article is available in PDF format.


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