Discrete artificial boundary conditions for nonlinear Schrödinger equations

@article{Zisowsky2008DiscreteAB,
  title={Discrete artificial boundary conditions for nonlinear Schr{\"o}dinger equations},
  author={Andrea Zisowsky and Matthias Ehrhardt},
  journal={Mathematical and Computer Modelling},
  year={2008},
  volume={47},
  pages={1264-1283}
}
In this work we construct and analyze discrete artificial boundary conditions (ABCs) for different finite difference schemes to solve nonlinear Schrödinger equations. These new discrete boundary conditions are motivated by the continuous ABCs recently obtained by the potential strategy of Szeftel. Since these new nonlinear ABCs are based on the discrete ABCs for the linear problem we first review the well–known results for the linear Schrödinger equation. We present our approach for a couple of… CONTINUE READING
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