Finite difference discretization of the cubic Schrödinger equation

@article{Akrivis1993FiniteDD,
  title={Finite difference discretization of the cubic Schr{\"o}dinger equation},
  author={Georgios Akrivis},
  journal={Ima Journal of Numerical Analysis},
  year={1993},
  volume={13},
  pages={115-124}
}
  • G. Akrivis
  • Published 1993
  • Mathematics
  • Ima Journal of Numerical Analysis
We analyze the discretization of an initial-boundary value problem for the cubic Schrodinger equation in one space dimension by a Crank-Nicolson-type finite difference scheme. We then linearize the corresponding equations at each time level by Newton's method and discuss an iterative modification of the linearized scheme which requires solving linear systems with the same tridiagonal matrix. We prove second-order error estimates 

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