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Journal of Applied Mathematics and Computing

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14-11-2021 | Original Research

Landweber iteration method for simultaneous inversion of the source term and initial data in a time-fractional diffusion equation

Authors: Jin Wen, Zhuan-Xia Liu, Chong-Wang Yue, Shi-Juan Wang

Published in: Journal of Applied Mathematics and Computing | Issue 5/2022

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Abstract

The present paper is devoted to identifying the space-dependent source term and initial value simultaneously for a time-fractional diffusion equation. This inverse problem is reformulated on the basis of Fourier method as operator equations of the first kind. The construction of the solution to the inverse problem is derived by using the Landweber iteration method for the solution of the corresponding conjugate operator equation. In this paper, we also present error estimates between the exact solution and the regularized solution by the a priori and the a posteriori parameter choice rules. Numerical verification on the efficiency and accuracy of the proposed algorithm is performed by solving three numerical examples in one-dimensional and two-dimensional cases.

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Title: Landweber iteration method for simultaneous inversion of the source term and initial data in a time-fractional diffusion equation
Authors: Jin Wen
Zhuan-Xia Liu
Chong-Wang Yue
Shi-Juan Wang
Publication date: 14-11-2021
Publisher: Springer Berlin Heidelberg
Published in: Journal of Applied Mathematics and Computing / Issue 5/2022
Print ISSN: 1598-5865
Electronic ISSN: 1865-2085
DOI: https://doi.org/10.1007/s12190-021-01656-0

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