Resonance-based schemes for dispersive equations via decorated trees

@article{Bruned2022ResonancebasedSF,
  title={Resonance-based schemes for dispersive equations via decorated trees},
  author={Yvain Bruned and Katharina Schratz},
  journal={Forum of Mathematics, Pi},
  year={2022},
  volume={10}
}
Abstract We introduce a numerical framework for dispersive equations embedding their underlying resonance structure into the discretisation. This will allow us to resolve the nonlinear oscillations of the partial differential equation (PDE) and to approximate with high-order accuracy a large class of equations under lower regularity assumptions than classical techniques require. The key idea to control the nonlinear frequency interactions in the system up to arbitrary high order thereby lies in… 
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