Long-term stability of variable stepsize approximations of semigroups
Open Access
- 3 August 2001
- journal article
- Published by American Mathematical Society (AMS) in Mathematics of Computation
- Vol. 71 (240), 1545-1568
- https://doi.org/10.1090/s0025-5718-01-01389-8
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.Keywords
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