Numerical Identification of a Time-Dependent Coefficient in a Time-Fractional Diffusion Equation with Integral Constraints

Abstract

In this paper, we numerically address the inverse problem of identifying a time-dependent coefficient in the time-fractional diffusion equation. An a priori estimate is established to ensure uniqueness and stability of the solution. A fully implicit finite-difference scheme is proposed and rigorously analysed for stability and convergence. An efficient algorithm based on an integral formulation is implemented and verified through numerical experiments, demonstrating accuracy and robustness under noisy data.

References in corpus (3)

• A second-order scheme with nonuniform time steps for a linear reaction-sudiffusion problem
• Recovering the Potential and Order in One-Dimensional Time-Fractional Diffusion with Unknown Initial Condition and Source
• Inverse source problems for a multidimensional time-fractional wave equation with integral overdetermination conditions