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://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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