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Long-term stability of variable stepsize approximations of semigroups
Author(s):
Nikolai
Bakaev;
Alexander
Ostermann.
Journal:
Math. Comp.
71
(2002),
1545-1567.
MSC (2000):
Primary 65M12, 65L20
Posted:
August 3, 2001
MathSciNet review:
1933044
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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:
10.1090/S0025-5718-01-01389-8
PII:
S 0025-5718(01)01389-8
Received by editor(s):
July 10, 2000
Received by editor(s) in revised form:
December 26, 2000
Posted:
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
Copyright of article:
Copyright
2001,
American Mathematical Society
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