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

Anatoly B. Bakushinsky; Mikhail Yu. Kokurin; Mikhail M. Kokurin

doi:10.1515/jiip.2011.015

Published by De Gruyter April 2, 2011

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

Anatoly B. Bakushinsky , Mikhail Yu. Kokurin and Mikhail M. Kokurin

From the journal Journal of Inverse and Ill-posed Problems

https://doi.org/10.1515/jiip.2011.015

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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

Received: 2010-09-26

Published Online: 2011-04-02

Published in Print: 2011-March

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

Abstract

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