A functional calculus approach for the rational  approximation with nonuniform partitions

Hassan Emamirad; Arnaud Rougirel

doi:10.3934/dcds.2008.22.955

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2008, Volume 22, Issue 4: 955-972. Doi: 10.3934/dcds.2008.22.955

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A functional calculus approach for the rational approximation with nonuniform partitions

Hassan Emamirad^1, and
Arnaud Rougirel^1,

1.
Laboratoire de Mathématiques et Applications, Université de Poitiers & CNRS, Téléport 2 - BP 30179, 86 962 Futuroscope Chasseneuil Cedex

Received: August 31, 2007

Revised: October 31, 2007

Published: September 2008

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Abstract

By introducing $M$-functional calculus we generalize some results of Brenner and Thomée on the stability and convergence of rational approximation schemes of bounded semigroups for nonuniform time steps. We give also the rate of convergence for the approximation of the time derivative of these semigroups.

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Mathematics Subject Classification: 65M12, 65J10.

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