Regularization methods for solving a time-fractional diffusion inverse source problem

Hanghang Wu and Hongqi Yang

Mathematics and Computers in Simulation (MATCOM), 2025, vol. 232, issue C, 295-310

Abstract: This paper studies a time-fractional diffusion ill-posed inverse source problem. We use a simplified Tikhonov regularization method and a Fourier regularization method to solve the problem. Under the selection rules of a priori and a posteriori regularization parameters, a priori and a posteriori error estimates are derived. Among them, the a priori error estimate derived from the simplified Tikhonov regularization method is optimal, while the a posteriori error estimate is quasi-optimal. The a priori and a posteriori error estimates derived by the Fourier regularization method are both optimal. Finally, numerical examples are conducted to demonstrate the effectiveness and stability of the proposed regularization methods.

Keywords: Time-fractional diffusion equation; Inverse problem; Identifying the source term; Regularization method; Optimal error bound (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378475425000023
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:232:y:2025:i:c:p:295-310

DOI: 10.1016/j.matcom.2025.01.002

Access Statistics for this article

Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens

More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier
Bibliographic data for series maintained by Catherine Liu ().