Convolution quadrature revisited
type: Item
instance of: scholarly article
title: Convolution quadrature revisited
zbMATH Open document ID: 1083.65123
author: Christian Lubich
published in: BIT
publication date: 2005-04-07T00:00:00Z
review text: This paper is a review on convolution quadratures. In fact they have many attractive features that let them work well in a lot of applications where the model equations are derived via a frequency-domain fundamental solution of the transfer equation, whereas the time-domain fundamental solution or impulse response is not available. Moreover such convolution quadrature methods enjoy excellent stability properties when used to discretize integral, integro-differential equations or integro-partial differential equations, etc. They are also useful as a theoretical tool in analyzing standard numerical time discretization methods through discretized operational calculus. In particular this paper closes a gap that was left in the theory of \textit{C. Lubich} [Numer. Math. 52, 129--145 (1988; Zbl 0637.65016)], by extending the known approximation results for the case of sectorial Laplace transforms to finite-part convolutions with nonintegrable kernel. The author also presents two new detailed and unified proofs of the optimal error bounds for both locally integrable and nonintegrable convolution kernels.
reviewed by: Paola Lamberti
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45K05
Mathematics Subject Classification ID: 45E10
zbMATH DE Number: 2153690
zbMATH Keywords: discretized operational calculus
zbMATH Keywords: linear multistep methods
zbMATH Keywords: stability
zbMATH Keywords: integro-differential equations
zbMATH Keywords: numerical time discretization methods
zbMATH Keywords: sectorial Laplace transforms
zbMATH Keywords: finite-part convolutions
zbMATH Keywords: error bounds
MaRDI profile type: Publication
full work available at URL: b:bitn.0000046813.23911.2d
OpenAlex ID: W2031029580
DOI: 10.1023/B:BITN.0000046813.23911.2D
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description: scientific article; zbMATH DE number 2153690