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Stability of rational multistep approximations of holomorphic semigroups

Author: C. Palencia
Journal: Math. Comp. 64 (1995), 591-599
MSC: Primary 65J10; Secondary 34G10, 47D06, 65M12
MathSciNet review: 1277770
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Abstract: In this paper we prove the stability of semidiscretizations in time of holomorphic semigroups in Banach spaces by means of $ {\text{A}}(\alpha )$-stable rational multistep methods. No assumptions on the method other than $ {\text{A}}(\alpha )$-stability are required. Our result is applicable in the maximum norm analysis of parabolic problems.

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Keywords: Parabolic problems, holomorphic semigroups, analytic semigroups, multistep and rational methods, stability, $ {\text{A}}(\alpha )$-stability, maximum norm, Banach spaces
Article copyright: © Copyright 1995 American Mathematical Society

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