Geodesic
The necessary and sufficient conditions for the qualified convergence of difference methods for approximate solution of the ill-posed Cauchy problem in a~Banach space
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2009), pp. 56-60

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We study properties of the finite-difference methods for approximate solution of the ill-posed Cauchy problem for a homogeneous equation of the first order with a sectorial operator in a Banach space. We obtain the necessary and sufficient conditions for the qualified (with respect to the step of grid) uniform (on a segment) convergence of approximations to the exact solution of the problem. These conditions represent a priori data about the segment, where a solution exists, or about the sourcewise representation of a certain value of the desired solution.
Keywords: Cauchy problem, ill-posed problem, finite-difference approximation methods, sectorial condition, Banach space
Mots-clés : sourcewise representation. 
@article{IVM_2009_4_a7,
     author = {V. V. Klyuchev},
     title = {The necessary and sufficient conditions for the qualified convergence of difference methods for approximate solution of the ill-posed {Cauchy} problem in {a~Banach} space},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {56--60},
     publisher = {mathdoc},
     number = {4},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2009_4_a7/}
}
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V. V. Klyuchev. The necessary and sufficient conditions for the qualified convergence of difference methods for approximate solution of the ill-posed Cauchy problem in a~Banach space. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2009), pp. 56-60. http://geodesic.mathdoc.fr/item/IVM_2009_4_a7/