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Journal Articles Computational Mathematics and Mathematical Physics Year : 2013

Geometric numerical schemes for the KdV equation


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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hal-00694896 , version 1 (07-05-2012)


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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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