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Sib. Èlektron. Mat. Izv., 2015, Volume 12, Pages 28–44 (Mi semr567)  

This article is cited in 3 scientific papers (total in 3 papers)

Computational mathematics

Stability of three-layer difference scheme

M. A. Sultanov

Kh. Yasavi International Kazakh-Turkish University

Abstract: The stability of a three-layer difference scheme with two weights approximating the ill-posed Cauchy problem for second order differential equation with an unbounded, both above and below the self-adjoint operator in the main part are considered. Based on the factorization method and application variants weight difference of a priori estimates of Carleman type conditions unconditional stability of the scheme has been obtained. Application of the above theorem to construct unconditionally stable difference schemes for the one-dimensional coefficient inverse problem of determining the potential in the Schrodinger equation is considered.

Keywords: finite-difference scheme, stability, the difference operator, weighted a priori estimates of Carleman type, inverse problem, eigenvalues, eigenfunctions.

DOI: https://doi.org/10.17377/semi.2015.12.004

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UDC: 519.6
MSC: 65Q10
Received January 10, 2014, published January 22, 2015

Citation: M. A. Sultanov, “Stability of three-layer difference scheme”, Sib. Èlektron. Mat. Izv., 12 (2015), 28–44

Citation in format AMSBIB
\Bibitem{Sul15}
\by M.~A.~Sultanov
\paper Stability of three-layer difference scheme
\jour Sib. \`Elektron. Mat. Izv.
\yr 2015
\vol 12
\pages 28--44
\mathnet{http://mi.mathnet.ru/semr567}
\crossref{https://doi.org/10.17377/semi.2015.12.004}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. S. Berdyshev, M. A. Sultanov, “On stability of the solution of multidimensional inverse problem for the Schrodinger equation”, Math. Model. Nat. Phenom., 12:3, SI (2017), 119–133  crossref  mathscinet  zmath  isi  scopus
    2. M. A. Sultanov, M. I. Akylbaev, R. Ibragimov, “Conditional stability of a solution of a difference scheme for an ill-posed Cauchy problem”, Electron. J. Differ. Equ., 2018, 33  mathscinet  zmath  isi
    3. M. A. Sultanov, M. I. Akylbaev, “Construction of unconditionally stable difference schemes based on stability of perturbed difference scheme”, Third International Conference of Mathematical Sciences (Icms 2019), AIP Conf. Proc., 2183, eds. H. Cakalli, L. Kocinac, R. Harte, V. Cavalcanti, A. Ashyralyev, I. Sakalli, I. Canak, O. Gurtug, M. Cavalcanti, D. Turkoglu, M. Tez, H. Kandemir, S. Uyaver, K. Akay, I. Gul, T. Yilmazturk, T. Akyel, F. Ucgun, H. Sahin, Amer. Inst. Phys., 2019, UNSP 070026  crossref  isi  scopus
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