MODIFIED LANDWEBER ITERATIVE METHOD FOR A BACKWARD PROBLEM IN TIME OF THE DIFFUSION EQUATION WITH LOCAL AND NONLOCAL OPERATORS

  • Hongwu ZHANG ,
  • Yanhui LI
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  • School of Mathematics and Information Science, North Minzu University, Yinchuan 750021, China
Hongwu ZHANG, E-mail: zh-hongwu@163.com

Received date: 2023-10-26

  Revised date: 2024-03-18

  Online published: 2025-09-30

Supported by

NSF of Ningxia (2022AAC03234), the NSF of China (11761004), the Construction Project of First-Class Disciplines in Ningxia Higher Education (NXYLXK2017B09), and the Postgraduate Innovation Project of North Minzu University (YCX23074).

Abstract

In this article, we consider a backward problem in time of the diffusion equation with local and nonlocal operators. This inverse problem is ill-posed because the solution does not depend continuously on the measured data. Inspired by the classical Landweber iterative method and Fourier truncation technique, we develops a modified Landweber iterative regularization method to restore the continuous dependence of solution on the measurement data. Under the a-priori and a-posteriori choice rules for the regularized parameter, the convergence estimates for the regularization method are derived. Some results of numerical simulation are provided to verify the stability and feasibility of our method in dealing with the considered problem.

Cite this article

Hongwu ZHANG , Yanhui LI . MODIFIED LANDWEBER ITERATIVE METHOD FOR A BACKWARD PROBLEM IN TIME OF THE DIFFUSION EQUATION WITH LOCAL AND NONLOCAL OPERATORS[J]. Acta mathematica scientia, Series B, 2025 , 45(3) : 1205 -1222 . DOI: 10.1007/s10473-025-0324-2

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