Geometric numerical schemes for the KdV equation

Abstract : 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.
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Dernière modification le : lundi 21 mars 2016 - 11:33:23
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Denys Dutykh, Marx Chhay, Francesco Fedele. Geometric numerical schemes for the KdV equation. Computational Mathematics and Mathematical Physics, 2013, 53 (2), pp.221-236. 〈10.1134/S0965542513020103〉. 〈hal-00694896〉

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