TITLE:
The Tikhonov Regularization Method in Hilbert Scales for Determining the Unknown Source for the Modified Helmholtz Equation
AUTHORS:
Lei You, Zhi Li, Juang Huang, Aihua Du
KEYWORDS:
Ill-Posed Problem, Unknown Source, Regularization Method, Discrepancy Principle in Hilbert Scales
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.4 No.1,
January
27,
2016
ABSTRACT: In this paper, we consider an unknown source problem for the modified Helmholtz equation. The Tikhonov regularization method in Hilbert scales is extended to deal with ill-posedness of the problem. An a priori strategy and an a posteriori choice rule have been present to obtain the regularization parameter and corresponding error estimates have been obtained. The smoothness parameter and the a priori bound of exact solution are not needed for the a posteriori choice rule. Numerical results are presented to show the stability and effectiveness of the method.