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PreprintCC BY-NC-ND 4.0arXiv

Numerical Analysis of Space-Time Dependent Source Identification in Subdiffusion Equations

  • Siyu Cen
  • Bangti Jin
  • Yavar Kian
  • Zhi Zhou
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Abstract

In this work, we propose an easy-to-implement fixed-point algorithm for reconstructing a space-time dependent source in a subdiffusion model from lateral boundary measurements. The numerical scheme combines a Galerkin finite element method for spatial discretization with a finite difference method for temporal discretization. We establish the linear convergence of the fixed-point iteration and derive an error bound that depends explicitly on the discretization parameters and the noise level. The error analysis relies on stability properties of the continuous inverse problem and technical estimates for the associated direct problem with limited-regularity data. Numerical experiments are presented to support and complement the theoretical analysis.

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Cite

BibTeXRIS
BibTeX
@misc{cen2026numerical,
  title = {{Numerical Analysis of Space-Time Dependent Source Identification in Subdiffusion Equations}},
  author = {Siyu Cen and Bangti Jin and Yavar Kian and Zhi Zhou},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2605.05579},
  eprint = {2605.05579},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.05579},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Numerical Analysis of Space-Time Dependent Source Identification in Subdiffusion Equations
AU  - Siyu Cen
AU  - Bangti Jin
AU  - Yavar Kian
AU  - Zhi Zhou
PY  - 2026
DA  - 2026/09/14
PB  - arXiv
DO  - 10.48550/arxiv.2605.05579
UR  - https://arxiv.org/abs/2605.05579
AB  - In this work, we propose an easy-to-implement fixed-point algorithm for reconstructing a space-time dependent source in a subdiffusion model from lateral boundary measurements. The numerical scheme combines a Galerkin finite element method for spatial discretization with a finite difference method for temporal discretization. We establish the linear convergence of the fixed-point iteration and derive an error bound that depends explicitly on the discretization parameters and the noise level. The error analysis relies on stability properties of the continuous inverse problem and technical estimates for the associated direct problem with limited-regularity data. Numerical experiments are presented to support and complement the theoretical analysis.
ER  -