A functional calculus approach for the rational approximation with nonuniform partitions
type: Item
instance of: scholarly article
title: A functional calculus approach for the rational approximation with nonuniform partitions
zbMATH Open document ID: 1152.65091
author: Hassan Emamirad
author: Arnaud Rougirel
published in: Discrete and Continuous Dynamical Systems
publication date: 2008-10-30T00:00:00Z
review text: The authors generalize some results of \textit{P. Brenner} and \textit{V. Thomée} [SIAM J. Numer. Anal. 16, 683--694 (1979; Zbl 0413.41011)] on the stability and convergence of rational approximation schemes of bounded semigroups for uniform time steps. The purpose of the paper is to approximate \( e^{tA}\) by suitable operators \(P_{n}(A)\) by using nonuniform partitions \(\tau_{1},...,\tau_{n}\) of the time interval [0,t]. If \(R\) is a rational function \[ P_{n}(A)=R(\tau_{1}A)... R(\tau_{n}A). \] The choice of rational functions is motivated by the fact that they appear in such important schemes as backward Euler and Crank-Nicolson. The paper is organized as follows: Notation and main assumptions; \textit{M}-functional calculus; On the rate of convergence; Sharpness of the Convergence Theorem; Approximation of the derivative; References(12).
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65M99
zbMATH DE Number: 5359502
zbMATH Keywords: strongly continuous semigroup
zbMATH Keywords: rate of convergence
zbMATH Keywords: Crank-Nicolson scheme
zbMATH Keywords: nonuniform partition
MaRDI profile type: Publication
full work available at URL: dcds.2008.22.955
OpenAlex ID: W2328839813
DOI: 10.3934/DCDS.2008.22.955
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description: scientific article; zbMATH DE number 5359502