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Stability of Implicit Difference Scheme for Solving the Identification Problem of a Parabolic Equation

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Numerical Analysis and Its Applications (NAA 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8236))

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Abstract

We consider the inverse problem of reconstructing the right side of a parabolic equation with an unknown time dependent source function. Numerical solution and well-posedness of this type problem with local boundary conditions considered previously by A.A. Samarskii, P.N. Vabishchevich and V.T. Borukhov. In this paper, we focus on studying the stability of the problem with nonlocal conditions. A stable algorithm for the approximate solution of the problem is presented.

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Authors and Affiliations

  1. Department of Mathematics, Fatih University, Istanbul, Turkey

    Abdullah Said Erdogan & Allaberen Ashyralyev

Authors
  1. Abdullah Said Erdogan
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  2. Allaberen Ashyralyev
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Editor information

Editors and Affiliations

  1. Institute of Information and Communication Technlogies, Bulgarian Academy of Sciences, Acad. G. Bonchev, Bl25A, 1113, Sofia, Bulgaria

    Ivan Dimov

  2. Department of Applied Analysis, Pázm\’{a}ny P\’{e}ter s\’{e}t\’{a}ny 1/C,, Eötvös Loránd University, 1117, Budapest, Hungary

    István Faragó

  3. University of Rousse, 8 Studentska Str.,, 7017, Rousse, Bulgaria

    Lubin Vulkov

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Erdogan, A.S., Ashyralyev, A. (2013). Stability of Implicit Difference Scheme for Solving the Identification Problem of a Parabolic Equation. In: Dimov, I., Faragó, I., Vulkov, L. (eds) Numerical Analysis and Its Applications. NAA 2012. Lecture Notes in Computer Science, vol 8236. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41515-9_29

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  • DOI: https://doi.org/10.1007/978-3-642-41515-9_29

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-41514-2

  • Online ISBN: 978-3-642-41515-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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