Geometric numerical schemes for the KdV equation
Résumé
Geometric discretizations that preserve certain Hamiltonian structures at the discrete level has been proven to enhance the accuracy of numerical schemes. In particular, numerous symplectic and multi-symplectic schemes have been proposed to solve numerically the celebrated Korteweg-de Vries (KdV) equation. In this work, we show that geometrical schemes are as much robust and accurate as Fourier-type pseudo-spectral methods for computing the long-time KdV dynamics, and thus more suitable to model complex nonlinear wave phenomena.
Domaines
Mécanique des fluides [physics.class-ph] Mécanique des fluides [physics.class-ph] Formation de Structures et Solitons [nlin.PS] Systèmes Solubles et Intégrables [nlin.SI] Physique Numérique [physics.comp-ph] Physique Atmosphérique et Océanique [physics.ao-ph] Dynamique des Fluides [physics.flu-dyn] Analyse numérique [math.NA]Origine | Fichiers produits par l'(les) auteur(s) |
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