Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

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
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 $C_0$ 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 $C_0$ 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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2000): 65M12, 65L20

Retrieve articles in all journals with MSC (2000): 65M12, 65L20


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: http://dx.doi.org/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
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