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

doi:10.1007/s12190-021-01656-0

	Landweber iteration method for simultaneous inversion of the source term and initial data in a time-fractional diffusion equation
	Wen, Jin 1; Liu, Zhuan-Xia 1; Yue, Chong-Wang 1; Wang, Shi-Juan2,3
	2022-10
发表期刊	Journal of Applied Mathematics and Computing
卷号	68 期号:5 页码:3219-3250
摘要	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. © 2021, Korean Society for Informatics and Computational Applied Mathematics.
关键词	Diffusion One dimensional Partial differential equations Iterative methods Parameterization Mathematical operators A priori and a posteriori parameter choice rule Conditional stability Landweber iteration Landweber iteration methods Operator equation Parameter choice rules Posteriori Simultaneous inversion Source terms Time fractional diffusion equation
DOI	10.1007/s12190-021-01656-0
收录类别	EI ; SCIE
ISSN	1598-5865
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000718221600001
出版者	Institute for Ionics
EI入藏号	20214711196091
EI主题词	Inverse problems
EI分类号	921 Mathematics ; 921.2 Calculus ; 921.6 Numerical Methods
原始文献类型	Journal article (JA)
EISSN	1865-2085
引用统计	被引频次：20[WOS] [WOS记录] [WOS相关记录]
文献类型	期刊论文
条目标识符	http://ir.lzufe.edu.cn/handle/39EH0E1M/33210
专题	信息工程与人工智能学院
作者单位	1.Department of Mathematics, Northwest Normal University, Lanzhou; 730070, China; 2.School of Traffic and Transportation, Lanzhou Jiaotong University, Lanzhou; 730070, China; 3.School of Information Engineering, Lanzhou University of Finance and Economics, Lanzhou; 730020, China
推荐引用方式 GB/T 7714	Wen, Jin,Liu, Zhuan-Xia,Yue, Chong-Wang,et al. Landweber iteration method for simultaneous inversion of the source term and initial data in a time-fractional diffusion equation[J]. Journal of Applied Mathematics and Computing,2022,68(5):3219-3250.
APA	Wen, Jin,Liu, Zhuan-Xia,Yue, Chong-Wang,&Wang, Shi-Juan.(2022).Landweber iteration method for simultaneous inversion of the source term and initial data in a time-fractional diffusion equation.Journal of Applied Mathematics and Computing,68(5),3219-3250.
MLA	Wen, Jin,et al."Landweber iteration method for simultaneous inversion of the source term and initial data in a time-fractional diffusion equation".Journal of Applied Mathematics and Computing 68.5(2022):3219-3250.