Author(s)

Lei You, Zhi Li, Juang Huang, Aihua Du

College of Science, Guangdong Ocean University, Zhanjiang, China.

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.

Ill-Posed Problem, Unknown Source, Regularization Method, Discrepancy Principle in Hilbert Scales

You, L. , Li, Z. , Huang, J. and Du, A. (2016) The Tikhonov Regularization Method in Hilbert Scales for Determining the Unknown Source for the Modified Helmholtz Equation. Journal of Applied Mathematics and Physics, 4, 140-148. doi: 10.4236/jamp.2016.41017.