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L. Banjai, C. Lubich, J. Melenk:
"Runge-Kutta convolution quadrature for operators arising in wave propagation";
Numerische Mathematik, 119 (2011).

An error analysis of Runge-Kutta convolution quadrature is presented
for a class of non-sectorial operators whose Laplace transform satisfies, besides the
standard assumptions of analyticity in a half-plane Re s > σ0 and a polynomial bound
O(|s|μ1 ) there, the stronger polynomial bound O(sμ2 ) in convex sectors of the form
| arg s| ≤ π/2 − θ for θ > 0. The order of convergence of the Runge-Kutta convolution
quadrature is determined by μ2 and the underlying Runge-Kutta method, but
is independent of μ1. Time domain boundary integral operators for wave propagation
problems have Laplace transforms that satisfy bounds of the above type. Numerical
examples from acoustic scattering show that the theory describes accurately the
convergence behaviour of Runge-Kutta convolution quadrature for this class of applications.
Our results show in particular that the full classical order of the Runge-Kutta
method is attained away from the scattering boundary.

http://dx.doi.org/10.007/s00211-011-0378-z