Work

A New Iteration Algorithm With Relaxation Factor for the Cauchy Problem of Time-fractional Diffusion Equation

Year: 2025

Type: article

Abstract: In this paper, we investigate a Cauchy problem for the time-fractional diffusion equation by using a new simplified iteration algorithm. The algorithm arises from the well-known Kozlov-Maz'ya iterative scheme for solving the Cauchy problem of classical ill-posed boundary value problems. A relaxation factor in the algorithm is introduced. Based on Fourier analysis, we give a choice rule for the relaxation factor. The iteration algorithm combined with a stopping criterion is given for stable numerical reconstruction of the solution. For illustration, several numerical experiments are constructed to demonstrate the feasibility and efficiency of the proposed method.

Source: Journal of Applied Analysis & Computation

DOI: 10.11948/20240354

Authors: Zhenping Li, Xiangtuan Xiong

Institutions: Luoyang Institute of Science and Technology, Northwest Normal University

Language: English

Topic: Numerical methods in inverse problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: Northwest Normal University, National Natural Science Foundation of China

Awards: G127874881, 梯度流方法在抛物方程系数重构问题中的应用研究, G848853407