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

doi:10.1007/s10473-025-0324-2

Abstract

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.

Key words: backward problem in time, diffusion equation with local and nonlocal operators, modified Landweber regularization, convergence estimate, numerical simulation

CLC Number:

35R25

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.

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