Long-term stability of variable stepsize approximations of semigroups

Bakaev, Nikolai; Ostermann, Alexander

doi:10.1090/S0025-5718-01-01389-8

Long-term stability of variable stepsize approximations of semigroups
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by Nikolai Bakaev and Alexander Ostermann PDF

Math. Comp. 71 (2002), 1545-1567 Request permission

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.

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