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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

6 Issues per year


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Online
ISSN
1569-3945
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Volume 16, Issue 6 (Jan 2008)

Issues

On error estimates of difference solution methods for ill-posed Cauchy problems in a Hilbert space

A. B. Bakushinsky
  • Institute for Systems Analysis of RAS, Moscow, Russia. Email:
/ M. Yu. Kokurin / S. K. Paymerov
Published Online: 2008-09-30 | DOI: https://doi.org/10.1515/JIIP.2008.029

Abstract

We consider an ill-posed Cauchy problem for an abstract linear differential equation of the first order in a Hilbert space. Both the operator and the initial state are supposed to be noisy. For solving the problem, a class of finite difference methods is used. Coordinating the mesh width with error levels we obtain logarithmic error estimates for the methods of this class.

Key words.: Ill-posed problem; operator differential equation; Cauchy problem; finite difference method; error estimates

About the article

Received: 2008-03-17

Published Online: 2008-09-30

Published in Print: 2008-10-01



Citation Information: Journal of Inverse and Ill-posed Problems, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/JIIP.2008.029. Export Citation

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[2]
A. B. Bakushinskii, M. M. Kokurin, and M. Yu. Kokurin
Proceedings of the Steklov Institute of Mathematics, 2013, Volume 280, Number S1, Page 53
[3]
Anatoly B. Bakushinsky, Mikhail Yu. Kokurin, and Mikhail M. Kokurin
Journal of Inverse and Ill-posed Problems, 2011, Volume 18, Number 9
[4]
Rolando Magnanini and Giorgio Talenti
Milan Journal of Mathematics, 2009, Volume 77, Number 1, Page 1

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