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Computational Algorithm for Identification of the Right-Hand Side of the Parabolic Equation

  • Petr N. Vabishchevich
  • Maria V. VasilyevaEmail author
  • Vasily I. Vasilyev
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9045)

Abstract

Among inverse problems for PDEs we distinguish coefficient inverse problems, which are associated with the identification of the right-hand side of an equation using some additional information. When considering time-dependent problems, the identification of the right-hand side dependences on space and on time is usually separated into individual problems. We have linear inverse problems; this situation essentially simplify their study. This work deals with the problem of determining in a multidimensional parabolic equation the right-hand side that depends on time only. To solve numerically a inverse problem we use standard finite difference approximations in space. The computational algorithm is based on a special decomposition, where the transition to a new time level is implemented via solving two standard elliptic problems.

Notes

Acknowledgements

This work was supported by RFBR (project 14-01-00785).

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Petr N. Vabishchevich
    • 1
    • 2
  • Maria V. Vasilyeva
    • 1
    • 2
    Email author
  • Vasily I. Vasilyev
    • 1
    • 2
  1. 1.Nuclear Safety InstituteMoscowRussia
  2. 2.North-Eastern Federal UniversityYakutskRussia

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