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International Conference on Numerical Analysis and Its Applications

NAA 2016: Numerical Analysis and Its Applications pp 220–226Cite as

Regularization Methods of the Continuation Problem for the Parabolic Equation

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10187))

Abstract

We investigate the one-dimensional continuation problem (the Cauchy problem) for the parabolic equation with the data on the part of the boundary. For numerical solution we apply finite-difference scheme inversion, the singular value decomposition and the gradient method of the minimizing the goal functional. The comparative analysis of numerical methods are presented.

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Acknowledgments

The work was supported by the RFBR (grants 14-01-00208, 16-01-00755 and 16-29-15120), the Ministry of Education and Science of the Russian Federation and the Ministry of Education and Science of the Republic of Kazakhstan (project 1746/GF4).

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Authors and Affiliations

  1. Institute of Computational Mathematics and Mathematical Geophysics, prospect Akademika Lavrentjeva, 6, Novosibirsk, 630090, Russia

    Andrey Belonosov & Maxim Shishlenin

  2. Sobolev Institute of Mathematics, 4 Acad. Koptyug Avenue, Novosibirsk, 630090, Russia

    Maxim Shishlenin

  3. Novosibirsk State University, 2 Pirogova Str., Novosibirsk, 630090, Russia

    Andrey Belonosov & Maxim Shishlenin

Authors
  1. Andrey Belonosov
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  2. Maxim Shishlenin
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Corresponding author

Correspondence to Maxim Shishlenin .

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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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Belonosov, A., Shishlenin, M. (2017). Regularization Methods of the Continuation Problem for the Parabolic Equation. 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_22

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  • DOI: https://doi.org/10.1007/978-3-319-57099-0_22

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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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