Geometric numerical schemes for the KdV equation

D. Dutykh, M. Chhay, F. Fedele

Research output: Contribution to journalArticlepeer-review

29 Scopus citations

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.

Original languageBritish English
Pages (from-to)221-236
Number of pages16
JournalComputational Mathematics and Mathematical Physics
Volume53
Issue number2
DOIs
StatePublished - 2013

Keywords

  • geometric numerical schemes
  • Hamiltonian structures
  • Korteweg-de Vries equation
  • pseudo-spectral methods
  • symplectic and multi-symplectic schemes
  • wave turbulence

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