An iterative method for an inverse source problem of time-fractional diffusion equation. Issue 10 (3rd October 2018)

• Record Type: Journal Article
• Authors: Wang, Jun-Gang; Ran, Yu-Hong
• Is Part Of: Inverse problems in science and engineering. Volume 26:Issue 10(2018)
• Page Start: 1509
• Page End: 1521
• Publication Date: 2018-10-03
• Subjects: Inverse source problem -- iteration method -- fractional diffusion equation -- convergence -- parameter choice rule; 65L09; Engineering mathematics -- Periodicals; Inverse problems (Differential equations) -- Periodicals; 620.001515357
• DOI: 10.1080/17415977.2017.1417406
• Languages: English
• ISSNs: 1741-5977

Abstract

Abstract: We propose an iteration method to recover a space-dependent source for a time-fractional diffusion equation from the final measurement. Based on the conditional stability of the inverse problem, we prove the convergence of the iterative regularization method under the a priori parameter choice rule and the a posteriori parameter choice rule, respectively. Numerical examples in one dimension and two dimension are given to validate the effectiveness of the presented method.