An error analysis of Runge-Kutta convolution quadrature

Lehel Banjai and Christian Lubich

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Submission date: 25. May. 2010
Pages: 13
published in: BIT : numerical mathematics, 51 (2011) 3, p. 483-496 
DOI number (of the published article): 10.1007/s10543-011-0311-y
Bibtex
MSC-Numbers: 65R20, 65L06, 65M15
Keywords and phrases: convolution quadrature, Runge-Kutta methods, Time-domain boundary integral operators
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Abstract:
An error analysis is given for convolution quadratures based on strongly A-stable Runge-Kutta methods, for the non-sectorial case of a convolution kernel with a Laplace transform that is polynomially bounded in a half-plane. The order of approximation depends on the classical order and stage order of the Runge-Kutta method and on the growth exponent of the Laplace transform. Numerical experiments with convolution quadratures based on the Radau IIA methods are given on an example of a time-domain boundary integral operator.