A note on a Cauchy problem for the Laplace equation: Regularization and error estimates |
| |
Authors: | Nguyen Huy Tuan Dang Duc Trong |
| |
Institution: | a Department of Mathematics, SaiGon University, 273 AnDuongVuong, HoChiMinh City, Viet Nam b Department of Mathematics, University of Natural Science, Viet Nam National University, 227 Nguyen Van Cu, Q.5, HoChiMinh City, Viet Nam |
| |
Abstract: | In this paper, a Cauchy problem for the Laplace equation is investigated. Based on the fundamental solution to the elliptic equation, we propose to solve this problem by the truncation method, which generates well-posed problem. Then the well posedness of the proposed regularizing problem and convergence property of the regularizing solution to the exact one are proved. Error estimates for this method are provided together with a selection rule for the regularization parameter. The numerical results show that our proposed numerical methods work effectively. This work extends to earlier results in Qian et al. (2008) 14] and Hao et al. (2009) 5]. |
| |
Keywords: | Elliptic equation Ill-posed problem Cauchy problem Contraction principle |
本文献已被 ScienceDirect 等数据库收录! |
|