Rational approximations of semigroups without scaling and squaring

Document Type

Article

Publication Title

Discrete and Continuous Dynamical Systems- Series A

Publication Date

11-1-2013

Abstract

We show that for all q ≥ 1 and 1 ≤ i ≤ q there exist pairwise conjugate complex numbers bq;i and q;i with Re(q;i) > 0 such that for any generator (A;D(A)) of a bounded, strongly continuous semigroup T(t) on Banach space X with resolvent R(A) := (I A)-1 the expression bq;1 t R( q;1 t ;A) + bq;2 t R( q;2 t ;A) + + bq;q t R( q;q t ;A) provides an excellent approximation of the semigroup T(t) on D(A2q-1). Precise error estimates as well as applications to the numerical inversion of the Laplace transform are given.

Volume

33

Issue

11-12

First Page

5305

Last Page

5317

DOI

10.3934/dcds.2013.33.5305

ISSN

10780947

E-ISSN

15535231

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