Contributions to Books:

L. Banjai, C. Lubich, J. Melenk:
"Runge-Kutta convolution quadrature for operators arising in wave propagation";
in: "ASC Report 24/2010", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2010, ISBN: 978-3-902627-03-2.

English abstract:
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
$\Re s > \sigma_0$ and a polynomial bound $\BigO(s^{\mu_1})$ there,
the stronger polynomial bound $\BigO(s^{\mu_2})$ in convex sectors of
the form $|\operatorname*{arg} s| \leq \pi/2-\theta < \pi/2$ for $\theta > 0$.
The order of convergence of the Runge-Kutta convolution quadrature is
determined by $\mu_2$ and the underlying Runge-Kutta method, but is
independent of $\mu_1$.
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.

Electronic version of the publication:

Created from the Publication Database of the Vienna University of Technology.