J. Melenk, A. Rieder:
"Runge-Kutta convolution quadrature and FEM-BEM coupling for the time-dependent linear Schrödinger equation";
Journal of Integral Equations and Applications, 29 (2017), S. 189 - 250.

Kurzfassung englisch:
We propose a numerical scheme to solve the time-dependent linear Schr"odinger equation. The discretization is carried out by combining a Runge-Kutta time stepping scheme with a finite element discretization in space. Since the Schr"odinger equation is posed on the whole space Rd, we combine the interior finite element discretization with a convolution quadrature based boundary element discretization. In this paper, we analyze the resulting fully discrete scheme in terms of stability and convergence rate. Numerical experiments confirm the theoretical findings.

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