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Finite-Difference Method for Solution of Advection Equation by Unstable Schemes

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Numerical Analysis and Its Applications (NAA 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10187))

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Abstract

In this work the analysis of two-layer differential schemes for the one-dimensional uniform linear equation of transfer is carried out: (a) the first finite-difference scheme is the UPWIND evolution scheme; (b) the second finite-difference scheme has central differential approximation of the convective term (Explicit Central Space evolution scheme); (c) the third scheme represents a downstream finite difference with a regularization term (Regularized Downwind evolution scheme). The special attention in this work is paid to a question of stability enhancement of differential schemes.

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References

  1. Samarskii, A.A.: The Theory of Difference Schemes. Marcel Dekker Inc., New York (2001)

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  2. Kalitkin, N.N.: Numerical Methods: Tutorial. BKhV-Peterburg Publ., St. Petersburg (2011). (in Russian)

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  3. Galanin, M.P., Savenkov, E.B.: Methods of Numerical Analysis of the Mathematical Models. Bauman MSTU Publ, Moscow (2010). (in Russian)

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Acknowledgements

This project has received funding from Russian Fund for Basic Researches (projects no. 15-01-04620-a, 16-07-00519-a).

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Authors and Affiliations

  1. Keldysh Institute of Applied Mathematics, 4 Miusskaya sq., 125047, Moscow, Russia

    Igor V. Popov

  2. National Research Nuclear University MEPhI, 31 Kashirskoe sh., 115409, Moscow, Russia

    Igor V. Popov

Authors
  1. Igor V. Popov
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Correspondence to Igor V. Popov .

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Editors and Affiliations

  1. Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Ivan Dimov

  2. Department of Applied Analysis, Eötvös Loránd University, Budapest, Hungary

    István Faragó

  3. Department of Applied Mathematics and Statistics, University of Rousse, Ruse, Bulgaria

    Lubin Vulkov

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Popov, I.V. (2017). Finite-Difference Method for Solution of Advection Equation by Unstable Schemes. In: Dimov, I., Faragó, I., Vulkov, L. (eds) Numerical Analysis and Its Applications. NAA 2016. Lecture Notes in Computer Science(), vol 10187. Springer, Cham. https://doi.org/10.1007/978-3-319-57099-0_63

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  • DOI: https://doi.org/10.1007/978-3-319-57099-0_63

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-57098-3

  • Online ISBN: 978-3-319-57099-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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