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.
Domains
Fluid mechanics [physics.class-ph] Fluids mechanics [physics.class-ph] Pattern Formation and Solitons [nlin.PS] Exactly Solvable and Integrable Systems [nlin.SI] Computational Physics [physics.comp-ph] Atmospheric and Oceanic Physics [physics.ao-ph] Fluid Dynamics [physics.flu-dyn] Numerical Analysis [math.NA]Origin | Files produced by the author(s) |
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