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Operator Semigroups for Convergence Analysis

  • Petra Csomós
  • István FaragóEmail author
  • Imre Fekete
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9045)

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.

Keywords

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

Notes

Acknowledgments

P. Csomós and I. Faragó kindly acknowledge the support of the bilateral Hungarian-Austrian Science and Technology program TET_10-1-2011-0728. I. Fekete was supported by the European Union and the State of Hungary, co-financed by the European Social Fund witihin the framework of TÁMOP-4.2.4.A/2-11/1-2012-0001 ‘National Program of Excellence’–convergence program.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.MTA-ELTE Numerical Analysis and Large Networks Research GroupHungarian Academy of SciencesBudapestHungary
  2. 2.Institute of MathematicsEötvös Loránd UniversityBudapestHungary
  3. 3.Department of Mathematics and Computer ScienceSzéchenyi István UniversityGyőrHungary

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