| Abstract: |
| In this talk, we will discuss the numerical recovery of both initial data and a spatially dependent potential in time-fractional subdiffusion models using observations at two different time levels. This problem is challenging because the coefficients-to-state map is more complex than for a single coefficient, and the decoupling method remains unclear. Our investigation addresses critical aspects of the numerical treatment and analysis of this inverse problem, including proving conditional stability, developing an efficient solver, and designing a discrete numerical scheme with a provable error estimate. We develop a fixed-point iterative algorithm to recover the initial data and potential together. By establishing novel \textsl{a priori} estimates for the discrete direct problem, we demonstrate the contraction mapping property of the fixed-point iteration, leading to both convergence of the iteration and error estimates for the fully discrete reconstruction. |
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