The Stability of Rational Approximations of Analytic Semigroups

On the Stability of Variable Stepsize Rational Approximations of Holomorphic Semigroups

We consider variable stepsize time approximations of holomorphic semigroups on general Banach spaces. For strongly A(0)-acceptable rational functions a general stability theorem is proved, which does not impose any constraint on the ratios between stepsizes.

Stability of Rational Multistep Approximations of Holomorphic Semigroups

In this paper we prove the stability of semidiscretizations in time of holomorphic semigroups in Banach spaces by means of A(a)-stable rational multistep methods. No assumptions on the method other than A(a)-stability are required. Our result is applicable in the maximum norm analysis of parabolic problems.

Long-term stability of variable stepsize approximations of semigroups

This paper is concerned with the stability of rational one-step approximations of C0 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 C0 semigroups are derived. The bounds are typica...

Stabilizations of the Trotter-kato Theorem and the Chernoff Product Formula

This paper concerns versions of the Trotter-Kato Theorem and the Chernoff Product Formula for C0-semigroups in the absence of stability. Applications to A-stable rational approximations of semigroups are presented.

Decidability and Tameness in the Theory of Finite Semigroups