Geodesic
Stability of three-layer difference scheme
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 28-44

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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. 
@article{SEMR_2015_12_a67,
     author = {M. A. Sultanov},
     title = {Stability of three-layer difference scheme},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {28--44},
     publisher = {mathdoc},
     volume = {12},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2015_12_a67/}
}
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M. A. Sultanov. Stability of three-layer difference scheme. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 28-44. http://geodesic.mathdoc.fr/item/SEMR_2015_12_a67/