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A Higher Order Difference Scheme for the Time Fractional Diffusion Equation with the Steklov Nonlocal Boundary Value Problem of the Second Kind

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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

We consider finite-difference schemes of higher order approximation for the time fractional diffusion equation with nonlocal boundary conditions containing real parameters \(\alpha \), \(\beta \) and \(\gamma \). We obtain a priori estimates for the solution of the difference problem, which imply the stability and convergence of the constructed difference schemes. The obtained results are supported by the numerical calculations carried out for some test problems as well.

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Acknowledgements

This work is executed under grant of the President of the Russian Federation for the state support of young Russian scientists MK–3360.2015.1.

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Authors and Affiliations

  1. Institute of Applied Mathematics and Automation, Russian Academy of Sciences, ul. Shortanova 89 a, Nalchik, 360000, Russia

    Anatoly A. Alikhanov

  2. Kabardino-Balkarian State University, ul. Chernyshevskogo 173, Nalchik, 360004, Russia

    Inna Z. Kodzokova

Authors
  1. Anatoly A. Alikhanov
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  2. Inna Z. Kodzokova
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Corresponding author

Correspondence to Anatoly A. Alikhanov .

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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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Alikhanov, A.A., Kodzokova, I.Z. (2017). A Higher Order Difference Scheme for the Time Fractional Diffusion Equation with the Steklov Nonlocal Boundary Value Problem of the Second Kind. 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_15

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  • DOI: https://doi.org/10.1007/978-3-319-57099-0_15

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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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