Approximation of Semigroups and Related Operator Functions by Resolvent Series

Gugat M, Grimm V (2010)


Publication Language: English

Publication Type: Journal article, Original article

Publication year: 2010

Journal

Publisher: Society for Industrial and Applied Mathematics

Book Volume: 48

Pages Range: 1826-1845

Journal Issue: 5

URI: http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=SJNAAM000048000005001826000001&idtype=cvips&gifs=yes

DOI: 10.1137/090768084

Abstract

We consider the approximation of semigroups e τA and of the functions ℓ j(τA) that appear in exponential integrators by resolvent series. The interesting fact is that the resolvent series expresses the operator functions e τA and ℓ j(τA), respectively, in efficiently computable terms. This is important for semigroups, where the new approximation is different from well-known approximations by rational functions, as well as for the application of exponential integrators, which are currently of high interest and which are usually studied in a semigroup setting on Banach spaces. The approximation of the operator functions ℓ j (τA) in a general, strongly continuous semigroup setting has not been discussed in the literature so far, but this is crucial for an application of these integrators with unbounded operators or bounded operators (like discretization matrices) with large norm and eigenvalues somewhere in the left half plane. © 2010 Society for Industrial and Applied Mathematics.

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APA:

Gugat, M., & Grimm, V. (2010). Approximation of Semigroups and Related Operator Functions by Resolvent Series. SIAM Journal on Numerical Analysis, 48(5), 1826-1845. https://dx.doi.org/10.1137/090768084

MLA:

Gugat, Martin, and Volker Grimm. "Approximation of Semigroups and Related Operator Functions by Resolvent Series." SIAM Journal on Numerical Analysis 48.5 (2010): 1826-1845.

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