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Computational Algorithm for Identification of the Right-Hand Side of the Parabolic Equation

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Finite Difference Methods,Theory and Applications (FDM 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9045))

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Abstract

Among inverse problems for PDEs we distinguish coefficient inverse problems, which are associated with the identification of the right-hand side of an equation using some additional information. When considering time-dependent problems, the identification of the right-hand side dependences on space and on time is usually separated into individual problems. We have linear inverse problems; this situation essentially simplify their study. This work deals with the problem of determining in a multidimensional parabolic equation the right-hand side that depends on time only. To solve numerically a inverse problem we use standard finite difference approximations in space. The computational algorithm is based on a special decomposition, where the transition to a new time level is implemented via solving two standard elliptic problems.

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Acknowledgements

This work was supported by RFBR (project 14-01-00785).

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Authors and Affiliations

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

    Petr N. Vabishchevich, Maria V. Vasilyeva & Vasily I. Vasilyev

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

    Petr N. Vabishchevich, Maria V. Vasilyeva & Vasily I. Vasilyev

Authors
  1. Petr N. Vabishchevich
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  2. Maria V. Vasilyeva
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  3. Vasily I. Vasilyev
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Corresponding author

Correspondence to Maria V. Vasilyeva .

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Editors and Affiliations

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

    Ivan Dimov

  2. Institue of Mathematics and MTA-ELTE Numerical Analysis and Large Networks Research Group, Eötvös Loránd University, Budapest, Hungary

    István Faragó

  3. University of Rousse, Rousse, Bulgaria

    Lubin Vulkov

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Vabishchevich, P.N., Vasilyeva, M.V., Vasilyev, V.I. (2015). Computational Algorithm for Identification of the Right-Hand Side of the Parabolic Equation. In: Dimov, I., Faragó, I., Vulkov, L. (eds) Finite Difference Methods,Theory and Applications. FDM 2014. Lecture Notes in Computer Science(), vol 9045. Springer, Cham. https://doi.org/10.1007/978-3-319-20239-6_43

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  • DOI: https://doi.org/10.1007/978-3-319-20239-6_43

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-20238-9

  • Online ISBN: 978-3-319-20239-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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