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The Mathemathical Background of Operator Splitting and the Effect of Non-Commutativity

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Large-Scale Scientific Computing (LSSC 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2179))

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Abstract

Operator splitting is a widely used procedure in the numerical solution of initial and boundary value problems of partial differential equations. In this paper the error of the operator splitting, the so-called splitting error, is investigated. The mathematical background of operator splitting is shortly discussed. Sufficient conditions, under which the splittingerror vanishes, are formulated for the splittingmetho d of the Danish Eulerian Model. The study is based on the L-commutativity of the operators used in the model. Finally, the size of the splitting error is analysed in the case where the splitted operators are linear.

This research was supported by the Hungarian National Research Fund OTKA under grant T031807

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References

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Authors and Affiliations

  1. ELTE University, Dept. Applied Analysis, H-1053, Budapest, Hungary

    I. Faragó & Á. Havasi

Authors
  1. I. Faragó
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  2. Á. Havasi
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Editor information

Editors and Affiliations

  1. Central Laboratory for Parallel Processing, Bulgarian Academy of Sciences, Acad G. Bontchev, 1113, Sofia, Bulgaria

    Svetozar Margenov

  2. DTU, UNI•C, Danish IT Centre for Education and Research, Bldg. 304, 2800, Lyngby, Denmark

    Jerzy Waśniewski

  3. University of Rousse, Studentska 8, 7017, Rousse, Bulgaria

    Plamen Yalamov

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© 2001 Springer-Verlag Berlin Heidelberg

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Faragó, I., Havasi, Á. (2001). The Mathemathical Background of Operator Splitting and the Effect of Non-Commutativity. In: Margenov, S., Waśniewski, J., Yalamov, P. (eds) Large-Scale Scientific Computing. LSSC 2001. Lecture Notes in Computer Science, vol 2179. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45346-6_27

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  • DOI: https://doi.org/10.1007/3-540-45346-6_27

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43043-8

  • Online ISBN: 978-3-540-45346-8

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