Inverse source problem for time fractional diffusion with discrete random noise

TL;DR

This paper addresses the ill-posed inverse source problem in a time fractional diffusion equation, proposing a regularization method using trigonometric techniques and analyzing its convergence rate.

Contribution

It introduces a novel regularization approach combining trigonometric methods with truncated expansions for this specific inverse problem.

Findings

The proposed method effectively stabilizes the solution.

Convergence rate of the regularization method is established.

Numerical experiments demonstrate the method's accuracy.

Abstract

In this paper, we deal with the inverse source problem of determining a source in a time fractional diffusion equation where data are given at a fixed time. This problem is ill-posed, i.e., the solution does not depend continuously on the data. To regularize the instable solution, we use the trigonometric method in nonparametric regression associated with the truncated expansion method. We also investigate the convergence rate.