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

TL;DR

This paper develops a numerical method for identifying a time-dependent coefficient in a time-fractional diffusion equation, ensuring stability, convergence, and robustness through analysis and experiments.

Contribution

It introduces a new integral formulation-based algorithm with rigorous stability and convergence analysis for inverse coefficient identification.

Findings

Algorithm achieves high accuracy with noisy data

Method demonstrates stability and convergence in numerical experiments

Effective in solving inverse problems for fractional diffusion equations

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.