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arXiv · 1205.1418

Geometric numerical schemes for the KdV equation

Denys Dutykh·Marx Chhay·Francesco Fedele
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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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Denys Dutykh, Marx Chhay, Francesco Fedele. 2012-05-07. Geometric numerical schemes for the KdV equation. https://doi.org/10.1134/s0965542513020103

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