Summation by parts for finite difference approximations for d/dx
Journal of Computational Physics
A stable and conservative interface treatment of arbitrary spatial accuracy
Journal of Computational Physics
Summation by parts operators for finite difference approximations of second derivatives
Journal of Computational Physics
On the order of accuracy for difference approximations of initial-boundary value problems
Journal of Computational Physics
Journal of Computational Physics
Stable Boundary Treatment for the Wave Equation on Second-Order Form
Journal of Scientific Computing
Stable and Accurate Interpolation Operators for High-Order Multiblock Finite Difference Methods
SIAM Journal on Scientific Computing
Journal of Scientific Computing
High-fidelity numerical solution of the time-dependent Dirac equation
Journal of Computational Physics
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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.