Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1704733 | Applied Mathematical Modelling | 2011 | 15 Pages |
Abstract
In this paper, we investigate a Cauchy problem associated with Helmholtz-type equation in an infinite “strip”. This problem is well known to be severely ill-posed. The optimal error bound for the problem with only nonhomogeneous Neumann data is deduced, which is independent of the selected regularization methods. A framework of a modified Tikhonov regularization in conjunction with the Morozov’s discrepancy principle is proposed, it may be useful to the other linear ill-posed problems and helpful for the other regularization methods. Some sharp error estimates between the exact solutions and their regularization approximation are given. Numerical tests are also provided to show that the modified Tikhonov method works well.
Related Topics
Physical Sciences and Engineering
Engineering
Computational Mechanics
Authors
Xiao-Li Feng, Chu-Li Fu, Hao Cheng,