Journal of Inverse and Ill-posed Problems
Editor-in-Chief: Kabanikhin, Sergey I.
6 Issues per year
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On the approximations of derivatives of integrated semigroups. II
This paper is devoted to the regularization in the process of approximation of values of unbounded operators in Banach spaces. More precisely, we consider the approximations of unbounded generators of C 0-semigroups and integrated semigroups. We consider M. M. Lavrentiev's method. Some iterative procedures are also investigated. It is shown that in general Banach spaces the approximation of the values of unbounded operators converges in strong sense. The presentation is given in the abstract framework of the discrete approximation scheme, which includes finite element methods, finite difference schemes and projection methods.
Keywords.: Abstract differential equations; Banach spaces; C 0-semigroups; integrated semigroups; Trotter–Kato theorem; discretization methods; discrete semigroups; stability of difference schemes; Lavrentiev's method; regularization procedure; iterative methods; ill-posed problems