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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

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On the approximations of derivatives of integrated semigroups

1Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, P. R. China.

2Scientific Research Computer Center, Lomonosov Moscow State University, Vorobjevy Gory, Moscow, Russia.

3Scientific Research Computer Center, Lomonosov Moscow State University, Vorobjevy Gory, Moscow, Russia.

Citation Information: Journal of Inverse and Ill-posed Problems. Volume 18, Issue 5, Pages 515–550, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: 10.1515/jiip.2010.024, December 2010

Publication History

Received:
2010-07-21
Published Online:
2010-12-20

Abstract

This paper is devoted to regularization in the process of derivative's approximation of integrated semigroups in time variables. We consider the direct method and also the method based on A. N. Tikchonov's approach. It is shown that discrete derivative converges in strong sense and the order of convergence in general Banach space is obtained. The presentation is given in the abstract framework of discrete approximation scheme, which includes finite element methods, finite difference schemes and projection methods.

Keywords: Abstract differential equations in Banach spaces; C0-semigroups; integrated semigroups; the Trotter–Kato theorem; discretization methods; stability of difference schemes; discrete semigroups; Banach spaces; regularization procedure; ill-posed problems

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