Fourth Order Time-stepping for Low Dispersion Korteweg-de Vries and Nonlinear

@inproceedings{Klein2008FourthOT,
  title={Fourth Order Time-stepping for Low Dispersion Korteweg-de Vries and Nonlinear},
  author={C. Klein},
  year={2008}
}
Purely dispersive equations, such as the Korteweg-de Vries and the nonlinear Schrödinger equations in the limit of small dispersion, have solutions to Cauchy problems with smooth initial data which develop a zone of rapid modulated oscillations in the region where the corresponding dispersionless equations have shocks or blowup. Fourth order time-stepping in combination with spectral methods is beneficial to numerically resolve the steep gradients in the oscillatory region. We compare the… CONTINUE READING
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