High Order Stable Finite Difference Methods for the Schrödinger Equation

Anna Nissen, Gunilla Kreiss, and Margot Gerritsen

May 2011

Abstract:

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.

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