A functional calculus approach for the rational approximation with nonuniform partitions

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December 2008, 22(4): 955-972. doi: 10.3934/dcds.2008.22.955

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, France, France

Received September 2007 Revised November 2007 Published September 2008

Abstract
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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.

Keywords: Nonuniform partition., Rate of convergence, Acceptable rational function, Functional calculus, Bounded strongly continuous semigroup, Crank-Nicholson scheme.

Mathematics Subject Classification: 65M12, 65J1.

Citation: Hassan Emamirad, Arnaud Rougirel. A functional calculus approach for the rational approximation with nonuniform partitions. Discrete & Continuous Dynamical Systems - A, 2008, 22 (4) : 955-972. doi: 10.3934/dcds.2008.22.955

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