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A Singularly Perturbed Boundary Value Problems with Fractional Powers of Elliptic Operators

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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

A boundary value problem for a fractional power \(0< \varepsilon < 1\) of the second-order elliptic operator is considered. The boundary value problem is singularly perturbed when \(\varepsilon \rightarrow 0\). It is solved numerically using a time-dependent problem for a pseudo-parabolic equation. For the auxiliary Cauchy problem, the standard two-level schemes with weights are applied. The numerical results are presented for a model two-dimensional boundary value problem with a fractional power of an elliptic operator. Our work focuses on the solution of the boundary value problem with \(0 < \varepsilon \ll 1\).

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Acknowledgements

This work was supported by the Russian Foundation for Basic Research (projects 14-01-00785, 15-01-00026).

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Authors and Affiliations

  1. Nuclear Safety Institute, 52, B. Tulskaya, 115191, Moscow, Russia

    Petr N. Vabishchevich

  2. North-Eastern Federal University, 58, Belinskogo, 677000, Yakutsk, Russia

    Petr N. Vabishchevich

Authors
  1. Petr N. Vabishchevich
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Correspondence to Petr N. Vabishchevich .

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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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Vabishchevich, P.N. (2017). A Singularly Perturbed Boundary Value Problems with Fractional Powers of Elliptic Operators. 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_13

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  • DOI: https://doi.org/10.1007/978-3-319-57099-0_13

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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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