Fan, Y., Guo, H.Z. and Li, X.X. (2011) The Simplified Tikhonov Regularization Method for Identifying the Unknown Source for the Modified Helmholtz Equation. Mathematical Problems in Engineering, 2011.

has been cited by the following article:

• 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.