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A Godunov-Ryabenkii Instability for a Quickest Scheme

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Numerical Analysis and Its Applications (NAA 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1988))

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Abstract

We consider a finite difference scheme, called Quickest, introduced by Leonard in 1979, for the convection-diffusion equation. Quickest uses an explicit, Leith-type differencing and third-order upwinding on the convective derivatives yielding a four-point scheme. For that reason the method requires careful treatment on the inflow boundary considering the fact that we need to introduce numerical boundary conditions and that they could lead us to instability phenomena. The stability region is found with the help of one of the most powerful methods for local analysis of the influence of boundary conditions - the Godunov-Ryabenkii theory.

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Authors and Affiliations

  1. Oxford University Computing Laboratory, Wolfson Building, Parks Road, Oxford OX1 3QD, England

    Ercília Sousa

Authors
  1. Ercília Sousa
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Editors and Affiliations

  1. Department of Computer Science, University of Rousse, 7000, Rousse, Bulgaria

    Lubin Vulkov  & Plamen Yalamov  & 

  2. UNI-C,Danish Computing Center for Research and Education, DTU,Building 304, 2800, Lyngby, Denmark

    Jerzy Waśniewski

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© 2001 Springer-Verlag Berlin Heidelberg

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Sousa, E. (2001). A Godunov-Ryabenkii Instability for a Quickest Scheme. In: Vulkov, L., Yalamov, P., Waśniewski, J. (eds) Numerical Analysis and Its Applications. NAA 2000. Lecture Notes in Computer Science, vol 1988. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45262-1_86

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  • DOI: https://doi.org/10.1007/3-540-45262-1_86

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41814-6

  • Online ISBN: 978-3-540-45262-1

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