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A new version of quasi-boundary value method for a 1-D nonlinear ill-posed heat problem
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P. H. Quan
Veröffentlicht/Copyright:
26. Januar 2010
Abstract
In this paper, a simple and convenient new regularization method which is called modified quasi-boundary value method for solving nonlinear backward heat equation is given. Some new quite sharp error estimates between the approximate solution are provided and generalize the results in our paper [Trong, Quan, Khanh, and Tuan, Zeitschrift Analysis und ihre Anwendungen 26: 231–245, 2007, Trong and Tuan, Electron. J. Diff. Eqns. 4: 1–10, 2006, Trong and Tuan, Electron. J. Diff. Eqns. 84: 1–12, 2008]. The approximation solution is calculated by the contraction principle. A numerical experiment is given.
Key words.: Backward heat problem; nonlinearly ill-posed problem; quasi-boundary value methods; quasi-reversibility methods; contraction principle
Received: 2009-04-14
Published Online: 2010-01-26
Published in Print: 2009-December
© de Gruyter 2009
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Artikel in diesem Heft
- An iterative regularization method for ill-posed Hammerstein type operator equation
- Sobolev error estimates and a priori parameter selection for semi-discrete Tikhonov regularization
- Complexity analysis of the iteratively regularized Gauss–Newton method with inner CG-iteration
- Regularization methods for a Cauchy problem for a parabolic equation in multiple dimensions
- A new version of quasi-boundary value method for a 1-D nonlinear ill-posed heat problem
Schlagwörter für diesen Artikel
Backward heat problem;
nonlinearly ill-posed problem;
quasi-boundary value methods;
quasi-reversibility methods;
contraction principle
Artikel in diesem Heft
- An iterative regularization method for ill-posed Hammerstein type operator equation
- Sobolev error estimates and a priori parameter selection for semi-discrete Tikhonov regularization
- Complexity analysis of the iteratively regularized Gauss–Newton method with inner CG-iteration
- Regularization methods for a Cauchy problem for a parabolic equation in multiple dimensions
- A new version of quasi-boundary value method for a 1-D nonlinear ill-posed heat problem
