Geometric numerical schemes for the KdV equation
Classical Physics
2013-04-23 v1 Numerical Analysis
Pattern Formation and Solitons
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.
Cite
@article{arxiv.1205.1418,
title = {Geometric numerical schemes for the KdV equation},
author = {Denys Dutykh and Marx Chhay and Francesco Fedele},
journal= {arXiv preprint arXiv:1205.1418},
year = {2013}
}
Comments
22 pages, 14 figures, 74 references. Other author's papers can be downloaded at http://www.lama.univ-savoie.fr/~dutykh/