Geodesic
On a~complete discretization scheme for an ill-posed Cauchy problem in a~Banach space
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 1, pp. 96-108

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A complete discretization scheme for an ill-posed Cauchy problem for abstract first-order linear differential equations with sectorial operators in a Banach space is validated. The scheme combines the time semidiscretization of the equations and a finite-dimensional approximation of the spaces and operators. Regularization properties of the scheme are established. Error estimates are obtained in the case of approximate initial data under various a priori assumptions concerning the solution.
Keywords: Cauchy problem, ill-posed problem, discretization, regularization, error estimate. 
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     title = {On a~complete discretization scheme for an ill-posed {Cauchy} problem in {a~Banach} space},
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A. B. Bakushinskii; M. M. Kokurin; M. Yu. Kokurin. On a~complete discretization scheme for an ill-posed Cauchy problem in a~Banach space. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 1, pp. 96-108. http://geodesic.mathdoc.fr/item/TIMM_2012_18_1_a7/