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- Title
On error estimates of difference solution methods for ill-posed Cauchy problems in a Hilbert space.
- Authors
Bakushinsky, A. B.; Kokurin, M. Yu; Paymerov, S. K.
- 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.
- Subjects
ERROR analysis in mathematics; CAUCHY problem; LINEAR differential equations; HILBERT space; NOISE
- Publication
Journal of Inverse & Ill-Posed Problems, 2008, Vol 16, Issue 6, p553
- ISSN
0928-0219
- Publication type
Article
- DOI
10.1515/JIIP.2008.029