Geometric numerical schemes for the KdV equation |
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Authors: | D Dutykh M Chhay F Fedele |
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Institution: | 1. Université de Savoie, Campus Scientifique, 73376, Le Bourget-du-Lac Cedex, France 2. School of Civil and Environmental Engineering and School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, USA
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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 equation. In this work, we show that geometrical schemes are as much robust and accurate as Fourier-type pseudospectral methods for computing the long-time KdV dynamics, and thus more suitable to model complex nonlinear wave phenomena. |
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