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A. Rieder:
"Semidiskrete transparente Randbedingungen für die Schrödingergleichung mittels Faltungsquadratur";
Supervisor: J. Melenk; Institut für Analysis und Scientific Computing, 2013; final examination: 2013-09-18.

The stability of a time discretization of the Schrodinger equation is studied. The Schrodinger equation, originally posed on the full space, is reduced to a bounded domain with the aid of transparent boundary conditions. The discretization of these boundary conditions is realized with convolution quadrature due to C. Lubich. A full error and stability analysis is performed for the case that the convolution quadrature is based on the implicit Euler method. For the more complicated case of a convolution quadrature based on an A-stable Runge-Kutta method, the impact of approximating the convolution quadrature weights by the trapezoidal rule is quantified, and the stability of the resulting method is ascertained. Numerical results illustrate the theoretical results.

http://publik.tuwien.ac.at/files/PubDat_225278.pdf