Runge-Kutta convolution quadrature and FEM-BEM coupling for the time   dependent linear Schr\"odinger equation
  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 $\R^d$ 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. 
Jens Markus Melenk, Alexander Rieder
math.NA