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Abstract
Rational generalizations of multistep schemes, where the linear stiff part of a given problem is treated by an A-stable rational approximation, have been proposed by several authors, but a reasonable convergence analysis for stiff problems has not been provided so far. In this paper we directly relate this approach to exponential multistep methods, a subclass of the increasingly popular class of exponential integrators. This natural, but new interpretation of rational multistep methods enables us to prove a convergence result of the same quality as for the exponential version. In particular, we consider schemes of rational Adams type based on A-acceptable Padé approximations to the matrix exponential. A numerical example is also provided.
Authors (2)
-
Winfried Auzinger
- Vienna University of Technology .
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- Category:
- Articles
- Type:
- artykuł w czasopiśmie wyróżnionym w JCR
- Published in:
-
BIT NUMERICAL MATHEMATICS
no. 52,
edition 1,
pages 3 - 20,
ISSN: 0006-3835 - Language:
- English
- Publication year:
- 2012
- Bibliographic description:
- Łapińska M., Auzinger W., Łapińska M.: Convergence of rational multistep methods of of Adams-Padé type// BIT NUMERICAL MATHEMATICS. -Vol. 52, iss. 1 (2012), s.3-20
- Verified by:
- Gdańsk University of Technology
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