Operator semigroups for convergence analysis

Petra Csomós, István Faragó, Imre Fekete

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The paper serves as a review on the basic results showing how functional analytic tools have been applied in numerical analysis. It deals with abstract Cauchy problems and present how their solutions are approximated by using space and time discretisations. To this end we introduce and apply the basic notions of operator semigroup theory. The convergence is analysed through the famous theorems of Trotter and Kato, Lax, and Chernoff. We also list some of their most important applications.

Original languageEnglish
Title of host publicationFinite Difference Methods, Theory and Applications - 6th International Conference, FDM 2014, Revised Selected Papers
EditorsIstvan Farago, Lubin Vulkov, Ivan Dimov
PublisherSpringer Verlag
Pages38-49
Number of pages12
ISBN (Print)9783319202389
DOIs
Publication statusPublished - 2015
Event6th International Conference on Finite Difference Methods, FDM 2014 - Lozenetz, Bulgaria
Duration: Jun 18 2014Jun 23 2014

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9045
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other6th International Conference on Finite Difference Methods, FDM 2014
CountryBulgaria
CityLozenetz
Period6/18/146/23/14

Keywords

  • Chernoff’s theorem
  • Convergence analysis
  • Lax equivalence theorem
  • Numerical analysis
  • Operator semigroups
  • Trotter-kato approximation theorem

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Csomós, P., Faragó, I., & Fekete, I. (2015). Operator semigroups for convergence analysis. In I. Farago, L. Vulkov, & I. Dimov (Eds.), Finite Difference Methods, Theory and Applications - 6th International Conference, FDM 2014, Revised Selected Papers (pp. 38-49). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9045). Springer Verlag. https://doi.org/10.1007/978-3-319-20239-6_4