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Operator Splitting with Spatial-temporal Discretization

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Spectral Theory, Mathematical System Theory, Evolution Equations, Differential and Difference Equations

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 221))

Abstract

Continuing earlier investigations, we analyze the convergence of operator splitting procedures combined with spatial discretization and rational approximations.

Mathematics Subject Classification (2000). 47D06, 47N40, 65J10.

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References

  1. W. Arendt, C. Batty, M. Hieber, F. Neubrander, Vector Valued Laplace Transforms and Cauchy Problems, Birkhäuser Verlag, Monographs in Mathematics 96, 2001.

    Google Scholar 

  2. A. Bátkai, P. Csomós, G. Nickel, Operator splittings and spatial approximations for evolution equations, J. Evolution Equations 9 (2009), 613-636, DOI 10.1007/s00028-009-0026-6.

    Article  MATH  Google Scholar 

  3. A. Bátkai, P. Csomós, B. Farkas, G. Nickel, Operator splitting for non-autonomous evolution equations, Journal of Functional Analysis 260 (2011), 2163-2190.

    Article  MathSciNet  MATH  Google Scholar 

  4. P. Csomós, G. Nickel, Operator splittings for delay equations, Computers and Mathematics with Applications 55 (2008), 2234-2246.

    Article  MathSciNet  MATH  Google Scholar 

  5. K.-J. Engel, R. Nagel, One-Parameter Semigroups for Linear Evolution Equations, Springer-Verlag, Berlin, 2000.

    MATH  Google Scholar 

  6. I. Faragó and Á. Havasi, Operator splittings and their applications, Mathematics Research Developments, Nova Science Publishers, New York, 2009.

    Google Scholar 

  7. M. Haase, The functional calculus for sectorial operators, Birkhäuser Verlag, Basel, 2006.

    Book  MATH  Google Scholar 

  8. E. Hairer, Ch. Lubich, G. Wanner, Geometric Numerical Integration. Structure-Preserving Algorithms for Ordinary Differential Equations, Springer-Verlag, Berlin, 2006.

    MATH  Google Scholar 

  9. H. Holden, K.H. Karlsen, K.-A. Lie, N.H. Risebro, Splitting Methods for Partial Differential Equations with Rough Solutions, European Mathematical Society, 2010.

    Google Scholar 

  10. W. Hundsdorfer, J. Verwer, Numerical solution of time-dependent advection-diffusion-reaction equations, Springer Series in Computational Mathematics 33, Springer-Verlag, Berlin, 2003.

    Google Scholar 

  11. K. Ito, F. Kappel, Evolution Equations and Approximations, World Scientific, River Edge, N.J., 2002.

    MATH  Google Scholar 

  12. K. Ito, F. Kappel, The Trotter-Kato theorem and approximation of PDE's, Mathematics of Computation 67 (1998), 21-44.

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Institute of Mathematics, Eötvös Loránd University, Pázmány P.sétány 1/C, H-1117, Budapest, Hungary

    András Bátkai

  2. Institut für Mathematik, Leopold-Franzens-Universität Innsbruck, Technikerstraße 13, A-6020, Innsbruck, Austria

    Petra Csomós

  3. Fachbereich Mathematik, Technische Universität Darmstadt, Schloßgartenstraße 7, D-64289, Darmstadt, Germany

    Bálint Farkas

  4. FB 6 Mathematik, Universität Siegen, Walter-Flex-Straße 3, D-57068, Siegen, Germany

    Gregor Nickel

Authors
  1. András Bátkai
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  2. Petra Csomós
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  3. Bálint Farkas
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  4. Gregor Nickel
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Corresponding author

Correspondence to András Bátkai .

Editor information

Editors and Affiliations

  1. , Abt. Mathematik V, Universität Ulm, Ulm, 89069, Germany

    Wolfgang Arendt

  2. Department of Mathematics, Virginia Polytechnic Institute, McBryde Hall 524, Blacksburg, 24061, Virginia, USA

    Joseph A. Ball

  3. Institut für Mathematik, AG Modellierung, Numerik und, TU Berlin, Straße des 17 Juni 136, Berlin, 10623, Berlin, Germany

    Jussi Behrndt

  4. Fak. II Mathematik & Naturwissenschaften, Institut für Mathematik, TU Berlin, Straße des 17. Juni 136, Berlin, 10623, Berlin, Germany

    Karl-Heinz Förster

  5. Fak. II Mathematik & Naturwissenschaften, Institut für Mathematik, TU Berlin, Straße des 17. Juni 136, Berlin, 10623, Berlin, Germany

    Volker Mehrmann

  6. , Institut für Mathematik, TU Ilmenau, Weimarer Str. 25, Ilmenau, 98693, Thüringen, Germany

    Carsten Trunk

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Bátkai, A., Csomós, P., Farkas, B., Nickel, G. (2012). Operator Splitting with Spatial-temporal Discretization. In: Arendt, W., Ball, J., Behrndt, J., Förster, KH., Mehrmann, V., Trunk, C. (eds) Spectral Theory, Mathematical System Theory, Evolution Equations, Differential and Difference Equations. Operator Theory: Advances and Applications, vol 221. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0297-0_9

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