Sib. Èlektron. Mat. Izv., 2015, Volume 12, Pages 28–44
This article is cited in 3 scientific papers (total in 3 papers)
Stability of three-layer difference scheme
M. A. Sultanov
Kh. Yasavi International Kazakh-Turkish University
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.
finite-difference scheme, stability, the difference operator, weighted a priori estimates of Carleman type, inverse problem, eigenvalues, eigenfunctions.
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Received January 10, 2014, published January 22, 2015
M. A. Sultanov, “Stability of three-layer difference scheme”, Sib. Èlektron. Mat. Izv., 12 (2015), 28–44
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\paper Stability of three-layer difference scheme
\jour Sib. \`Elektron. Mat. Izv.
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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
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
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
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