Regularization Methods of the Continuation Problem for the Parabolic Equation

  • Andrey Belonosov
  • Maxim ShishleninEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10187)


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.


Continuation problem Parabolic equation Numerical methods 



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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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Institute of Computational Mathematics and Mathematical GeophysicsNovosibirskRussia
  2. 2.Sobolev Institute of MathematicsNovosibirskRussia
  3. 3.Novosibirsk State UniversityNovosibirskRussia

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