@TechReport{	  it:2011-014,
  author	= {Anna Nissen and Gunilla Kreiss and Margot Gerritsen},
  title		= {High Order Stable Finite Difference Methods for the
		  {S}chr{\"o}dinger Equation},
  institution	= {Department of Information Technology, Uppsala University},
  department	= {Division of Scientific Computing},
  year		= {2011},
  number	= {2011-014},
  month		= may,
  abstract	= {In this paper we extend the
		  Summation-by-parts-simultaneous approximation term
		  (SBP-SAT) technique to the Schr{\"o}dinger equation.
		  Stability estimates are derived and the accuracy of
		  numerical approximations of interior order 2m, m=1, 2, 3,
		  are analyzed in the case of Dirichlet boundary conditions.
		  We show that a boundary closure of the numerical
		  approximations of order m lead to global accuracy of order
		  m+2. The results are supported by numerical simulations.}
}