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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Submitted on : Monday, May 7, 2012 - 9:04:04 AM
Last modification on : Thursday, June 28, 2018 - 12:38:02 PM
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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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