Advances in Computational Mathematics

, Volume 45, Issue 2, pp 735–755 | Cite as

A comparative analysis of numerical methods of solving the continuation problem for 1D parabolic equation with the data given on the part of the boundary

  • Andrey Belonosov
  • Maxim Shishlenin
  • Dmitriy KlyuchinskiyEmail author


The ill-posed continuation problem for the one-dimensional parabolic equation with the data given on the part of the boundary is investigated. We prove the uniqueness theorem about the solution of the continuation problem. The finite-difference scheme inversion, the singular value decomposition, and gradient type method are numerically compared. The influence of a noisy data on the solution is presented.


Parabolic equation Continuation problem Numerical methods Finite-difference scheme inversion Singular value decomposition Gradient method 

Mathematics Subject Classification (2010)

65M32 49N45 35K35 


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Authors kindly thank Professor Michael V. Klibanov for very careful remarks and comments which significantly helped us to improve the article.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Andrey Belonosov
    • 1
  • Maxim Shishlenin
    • 2
  • Dmitriy Klyuchinskiy
    • 1
    Email author
  1. 1.Institute of Computational Mathematics and Mathematical GeophysicsNovosibirsk State UniversityNovosibirskRussia
  2. 2.Institute of Computational Mathematics and Mathematical GeophysicsNovosibirsk State University, Sobolev Institute of MathematicsNovosibirskRussia

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