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J. Melenk, A. Rieder:
"On superconvergence of Runge-Kutta convolution quadrature for the wave equation";
in: "ASC Report 13/2019", herausgegeben von: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2019, ISBN: 978-3-902627-12-4, S. 1 - 18.

The semidiscretization of a sound soft scattering problem modelled by the wave equation is analyzed. The spatial treatment is done by integral equation methods.
Two temporal discretizations based on Runge-Kutta convolution quadrature are compared: one relying on the incoming wave as input data and one based on its temporal derivative. The convergence rate of the latter is shown to be higher than previously available results in the literature. Numerical results indicate sharpness of the analysis. When applying boundary element methods and convolution quadrature to the wave equation, it has been observed that for some quantities of
interest, the convergence rates established in the literature are not sharp. We prove a superconvergence result for sound-soft scattering.

http://www.asc.tuwien.ac.at/preprint/2019/asc13x2019.pdf