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An iterative method for the Cauchy problem for second-order elliptic equations
Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, Faculty of Science & Engineering.
Ivan Franko Natl Univ Lviv, Ukraine.
Ivan Franko Natl Univ Lviv, Ukraine.
Aston Univ, England.ORCID iD: 0000-0001-9066-7922
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2018 (English)In: International Journal of Mechanical Sciences, ISSN 0020-7403, E-ISSN 1879-2162, Vol. 142, p. 216-223Article in journal (Refereed) Published
Abstract [en]

The problem of reconstructing the solution to a second-order elliptic equation in a doubly-connected domain from knowledge of the solution and its normal derivative on the outer part of the boundary of the solution domain, that is from Cauchy data, is considered. An iterative method is given to generate a stable numerical approximation to this inverse ill-posed problem. The procedure is physically feasible in that boundary data is updated with data of the same type in the iterations, meaning that Dirichlet values is updated with Dirichlet values from the previous step and Neumann values by Neumann data. Proof of convergence and stability are given by showing that the proposed method is an extension of the Landweber method for an operator equation reformulation of the Cauchy problem. Connection with the alternating method is discussed. Numerical examples are included confirming the feasibility of the suggested approach.

Place, publisher, year, edition, pages
PERGAMON-ELSEVIER SCIENCE LTD , 2018. Vol. 142, p. 216-223
National Category
Applied Mechanics
Identifiers
URN: urn:nbn:se:liu:diva-149870DOI: 10.1016/j.ijmecsci.2018.04.042ISI: 000437372600019OAI: oai:DiVA.org:liu-149870DiVA, id: diva2:1236425
Available from: 2018-08-02 Created: 2018-08-02 Last updated: 2018-08-28

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Baravdish, George

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf