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# A functional calculus approach for the rational approximation with nonuniform partitions

• 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.
Mathematics Subject Classification: 65M12, 65J10.

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