Long-term stability of variable stepsize approximations of semigroups
Authors:
Nikolai Bakaev and Alexander Ostermann
Journal:
Math. Comp. 71 (2002), 1545-1567
MSC (2000):
Primary 65M12, 65L20
DOI:
https://doi.org/10.1090/S0025-5718-01-01389-8
Published electronically:
August 3, 2001
MathSciNet review:
1933044
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: This paper is concerned with the stability of rational one-step approximations of semigroups. Particular emphasis is laid on long-term stability bounds. The analysis is based on a general Banach space framework and allows variable stepsize sequences. Under reasonable assumptions on the stepsize sequence, asymptotic stability bounds for general
semigroups are derived. The bounds are typical in the sense that they contain, in general, a factor that grows with the number of steps. Under additional hypotheses on the approximation, more favorable stability bounds are obtained for the subclass of holomorphic semigroups.
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Additional Information
Nikolai Bakaev
Affiliation:
Department of Mathematics, Air Force Technical University, Planetnaya 3, Moscow 125190, Russia
Email:
bakaev@math.unige.ch, bakaev@postman.ru
Alexander Ostermann
Affiliation:
Section de mathématiques, Université de Genève, C.P. 240, CH-1211 Genève 24, Switzerland
Email:
Alexander.Ostermann@math.unige.ch
DOI:
https://doi.org/10.1090/S0025-5718-01-01389-8
Received by editor(s):
July 10, 2000
Received by editor(s) in revised form:
December 26, 2000
Published electronically:
August 3, 2001
Additional Notes:
The work of the first author was supported by the Swiss National Science Foundation under Grant 20-56577.99.
The second author was on leave from Universität Innsbruck, Institut für Technische Mathematik, Geometrie und Bauinformatik, Technikerstraße 13, A-6020 Innsbruck, Austria
Article copyright:
© Copyright 2001
American Mathematical Society