A Generalized Iterated Tikhonov Method in the Fourier Domain for Determining the Unknown Source of the Time-Fractional Diffusion Equation-Reference-Cited by-同舟云学术

A Generalized Iterated Tikhonov Method in the Fourier Domain for Determining the Unknown Source of the Time-Fractional Diffusion Equation

Published:2024-07-08 Issue:7 Volume:16 Page:864
ISSN:2073-8994
Container-title:Symmetry
language:en
Short-container-title:Symmetry

Author:

Zheng Bin¹,Liu Junfeng²,Zhao Zhenyu³,Dou Zhihong⁴,Gong Benxue³

Affiliation:

1. Business School, Shandong University of Technology, Zibo 255049, China

2. Mathematics Teaching Department, Tianjin RENAI College, Tianjin 301636, China

3. School of Mathematics and Statistics, Shandong University of Technology, Zibo 255049, China

4. Basic Course Department of Langfang Campus, Hebei University of Technology, Langfang 065099, China

Abstract

In this paper, an inverse problem of determining a source in a time-fractional diffusion equation is investigated. A Fourier extension scheme is used to approximate the solution to avoid the impact on smoothness caused by directly using singular system eigenfunctions for approximation. A modified implicit iteration method is proposed as a regularization technique to stabilize the solution process. The convergence rates are derived when a discrepancy principle serves as the principle for choosing the regularization parameters. Numerical tests are provided to further verify the efficacy of the proposed method.

Funder

This research was funded by Shandong University of Technology

Publisher

MDPI AG

Link

https://www.mdpi.com/2073-8994/16/7/864/pdf

Reference37 articles.

1. Podlubny, I. (1998). Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications, Elsevier.

2. Lazarević, M., Obradović, A., and Vasić, V. (2010, January 3–6). Robust finite-time stability analysis of fractional order time delay systems: New results. Proceedings of the 6th WSEAS International Conference on Dynamical Systems and Control, Control, Sousse, Tunisia.

3. Numerical solution of the space fractional Fokker–Planck equation;Liu;J. Comput. Appl. Math.,2004

4. Discrete random walk models for space–Time fractional diffusion;Gorenflo;Chem. Phys.,2002

5. Tarasov, V.E. (2008). Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media, Springer.