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

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