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On regularization and error estimates for the Cauchy problem of the modified inhomogeneous Helmholtz equation.
- Source :
- Journal of Inverse & Ill-Posed Problems; Oct2016, Vol. 24 Issue 5, p515-526, 12p
- Publication Year :
- 2016
-
Abstract
- In this paper, we consider the modified inhomogeneous Helmholtz equation Δ u( x, y) u( x, y) f( x, y), x , 0 y 1, with inhomogeneous Cauchy data being given at y 0. The problem is known to be ill-posed, as the solution (if exists) does not depend continuously on the given data. We propose a regularization method to obtain a stable approximate solution of the problem and get some error estimates. Finally, a numerical example shows the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 09280219
- Volume :
- 24
- Issue :
- 5
- Database :
- Complementary Index
- Journal :
- Journal of Inverse & Ill-Posed Problems
- Publication Type :
- Academic Journal
- Accession number :
- 118481346
- Full Text :
- https://doi.org/10.1515/jiip-2014-0069