Multisymplectic box schemes and the Korteweg – de Vries equation

@inproceedings{Ascher2003MultisymplecticBS,
  title={Multisymplectic box schemes and the Korteweg – de Vries equation},
  author={Uri M. Ascher and Robert I. McLachlan},
  year={2003}
}
We develop and compare some geometric integrators for the Korteweg-de Vries equation, especially with regard to their robustness for large steps in space and time, ∆x and ∆t, and over long times. A standard, semi-explicit, symplectic finite difference scheme is found to be fast and robust. However, in some parameter regimes such schemes are susceptible to developing small wiggles. At the same instances the fully implicit and multisymplectic Preissmann scheme, written as a 12-point box scheme… CONTINUE READING
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