A numerical method for solving retrospective inverse problem of fractional parabolic equation

An effective numerical method for solving the inverse problem of time fractional parabolic equation is constructed in this paper. We use implicit finite difference method to discretize the problem and for the inverse problem we propose a conjugate gradient type regularization method to solve the discretized ill-posed linear systems. By comparing the different errors and the results with different perturbed data in several numerical experiments, our method is shown to solve the inverse problem, even with some noisy measurements, efficiently and stably. (c) 2022 Elsevier B.V. All rights reserved.

Automated summary

An effective numerical method is proposed in this paper for solving the inverse problem of a time fractional parabolic equation. The method is shown to be efficient and stable in solving the inverse problem, even with noisy measurements, through numerical experiments.