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Iterative Solution of the Retrospective Inverse Problem for a Parabolic Equation Using the Conjugate Gradient Method

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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 theory and practice of the inverse problems for unsteady partial differential equations, significant attention is paid to the problems of determination of the initial condition based on the values of the initial function in a finite time.

In this paper, we propose a numerical method for the solution of a retrospective inverse problem for a multidimensional parabolic equation by a rapidly convergent conjugate gradient method. The results of computational experiments on model problems with quasi-solutions are being discussed. Besides, the results of computations obtained at specifying a perturbated additional condition with random errors are presented.

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Acknowledgement

The authors express their sincere gratitude to Professor P.N. Vabischevich for constructive comments and fruitful discussions.

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Authors and Affiliations

  1. North-Eastern Federal University, Yakutsk, Russia

    V. I. Vasil’ev & A. M. Kardashevsky

Authors
  1. V. I. Vasil’ev
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  2. A. M. Kardashevsky
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Corresponding authors

Correspondence to V. I. Vasil’ev or A. M. Kardashevsky .

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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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Vasil’ev, V.I., Kardashevsky, A.M. (2017). Iterative Solution of the Retrospective Inverse Problem for a Parabolic Equation Using the Conjugate Gradient Method. 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_80

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  • DOI: https://doi.org/10.1007/978-3-319-57099-0_80

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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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