Journal of Scientific Computing

, Volume 55, Issue 1, pp 173–199 | Cite as

High Order Stable Finite Difference Methods for the Schrödinger Equation



In this paper we extend the Summation-by-parts-simultaneous approximation term (SBP-SAT) technique to the Schrödinger 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.


Schrödinger equation High-order finite difference methods Summation-by-parts operators Numerical stability 


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© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of Energy Resources EngineeringStanford UniversityStanfordUSA
  2. 2.Department of Information TechnologyUppsala UniversityUppsalaSweden

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