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A quasi-boundary-value method for the Cauchy problem for elliptic equations with nonhomogeneous Neumann data.
- Source :
- Journal of Inverse & Ill-Posed Problems; 2010, Vol. 18 Issue 6, p617-645, 29p
- Publication Year :
- 2010
-
Abstract
- A Cauchy problem for elliptic equations with nonhomogeneous Neumann data in a cylindrical domain is investigated in this paper. For the theoretical aspect the a-priori and a-posteriori parameter choice rules are suggested and the corresponding error estimates are obtained. About the numerical aspect, for a simple case results given by two methods based on the discrete Sine transform and the finite difference method are presented; an idea of left-preconditioned GMRES (Generalized Minimum Residual) method is proposed to deal with the high dimensional case to save the time; a view of dealing with a general domain is suggested. Some ill-posed problems regularized by the quasi-boundary-value method are listed and some rules of this method are suggested. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 09280219
- Volume :
- 18
- Issue :
- 6
- Database :
- Complementary Index
- Journal :
- Journal of Inverse & Ill-Posed Problems
- Publication Type :
- Academic Journal
- Accession number :
- 56474824
- Full Text :
- https://doi.org/10.1515/JIIP.2010.028