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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.


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Online
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1569-3945
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Volume 18, Issue 9

Issues

On a class of finite difference methods for ill-posed Cauchy problems with noisy data

Anatoly B. Bakushinsky / Mikhail Yu. Kokurin / Mikhail M. Kokurin
Published Online: 2011-04-02 | DOI: https://doi.org/10.1515/jiip.2011.015

Abstract

We consider a class of finite difference schemes for approximating solutions to ill-posed Cauchy problems for first order linear operator differential equations in a Hilbert space. Both the operator and the initial state in the problems are supposed to be noisy. Using an appropriate coordination between the mesh width and error levels, we improve previous error estimates for approximations generated by the schemes.

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

About the article

Received: 2010-09-26

Published Online: 2011-04-02

Published in Print: 2011-03-01


Citation Information: Journal of Inverse and Ill-posed Problems, Volume 18, Issue 9, Pages 959–977, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/jiip.2011.015.

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[1]
A. B. Bakushinskii, M. M. Kokurin, and M. Yu. Kokurin
Proceedings of the Steklov Institute of Mathematics, 2013, Volume 280, Number S1, Page 53

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