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On a class of finite difference methods for ill-posed Cauchy problems with noisy data
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Anatoly B. Bakushinsky
,
Mikhail Yu. Kokurin
Published/Copyright:
April 2, 2011
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
© de Gruyter 2011
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Keywords for this article
Ill-posed problem;
operator differential equation;
Cauchy problem;
finite difference method;
error estimates
Articles in the same Issue
- Recent advances in analytical and numerical methods in inverse problems for PDEs (minisymposium report)
- On a class of finite difference methods for ill-posed Cauchy problems with noisy data
- Numerical algorithm for two-dimensional inverse acoustic problem based on Gel'fand–Levitan–Krein equation
- Some regularization methods for a thermoacoustic inverse problem
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