Conjugate gradient method for simultaneous identification of the source term and initial data in a time-fractional diffusion equation

Autor: Jin Wen, Zhuan-Xia Liu, Shan-Shan Wang
Jazyk: angličtina
Rok vydání: 2022
Předmět:
Zdroj: Applied Mathematics in Science and Engineering, Vol 30, Iss 1, Pp 324-338 (2022)
Druh dokumentu: article
ISSN: 2769-0911
27690911
DOI: 10.1080/27690911.2022.2075358
Popis: In this paper, we consider the simultaneous inversion of the source term and the initial data for a time-fractional diffusion equation based on the additional temperatures at two fixed times $ t=T_{1} $ and $ t=T_{2} $ . The inverse problem is formulated on the basis of the Fourier method as an operator equation of the first kind. For the overdetermined system of linear equations, we apply the conjugate gradient method with an appropriate stopping criterion to solve the least-squares problems. The method is not only able to converge quickly, but also it can solve large-scale linear equations. Based on the proposed results, it can be seen that the iteration numbers play a role of a regularization parameter. Four numerical examples are provided to demonstrate the effectiveness of the proposed method.
Databáze: Directory of Open Access Journals
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