Geometric numerical schemes for the KdV equation

Authors:
D. Dutykh;M. Chhay;F. Fedele
Affiliations:
Université de Savoie, Le Bourget-du-Lac Cedex, France 73376;Université de Savoie, Le Bourget-du-Lac Cedex, France 73376;School of Civil and Environmental Engineering and School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, USA
Venue:
Computational Mathematics and Mathematical Physics
Year:
2013

Citing 15
Cited 0

Numerical simulation of the stochastic Korteweg-de Vries equation

Physica D
Spectral methods in MatLab

Spectral methods in MatLab
Digital filters in adaptive time-stepping

ACM Transactions on Mathematical Software (TOMS)
On the long-time behaviour of soliton ensembles

Mathematics and Computers in Simulation - Nonlinear waves: computation and theory II
Multi-symplectic integration methods for Hamiltonian PDEs

Future Generation Computer Systems - Special issue: Geometric numerical algorithms
Multisymplectic box schemes and the Korteweg-de Vries equation

Applied Numerical Mathematics - Special issue: Workshop on innovative time integrators for PDEs
Local discontinuous Galerkin methods for nonlinear dispersive equations

Journal of Computational Physics
Backward error analysis for multisymplectic discretizations of Hamiltonian PDEs

Mathematics and Computers in Simulation - Special issue: Nonlinear waves: Computation and theory III
On Symplectic and Multisymplectic Schemes for the KdV Equation

Journal of Scientific Computing
Numerical studies of the stochastic Korteweg-de Vries equation

Journal of Computational Physics
Numerical solution of KdV-KdV systems of Boussinesq equations

Mathematics and Computers in Simulation
Dispersive properties of multisymplectic integrators

Journal of Computational Physics
On the partial difference equations of mathematical physics

IBM Journal of Research and Development
Adaptive time-stepping and computational stability

Journal of Computational and Applied Mathematics - Special issue: International workshop on the technological aspects of mathematics
Comparison of some Lie-symmetry-based integrators

Journal of Computational Physics

Quantified Score

Hi-index	0.00

Visualization

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.