The fractional Tikhonov regularization methods for identifying the initial value problem for a time-fractional diffusion equation

doi:10.1016/j.cam.2020.112998

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	The fractional Tikhonov regularization methods for identifying the initial value problem for a time-fractional diffusion equation
	Yang, Fan; Pu, Qu; Li, Xiao-Xiao
刊名	Journal of Computational and Applied Mathematics
	2020-12-15
卷号	380
关键词	Initial value problems Parameterization Partial differential equations Columnar axis Error estimates Exact solution Regularization parameters Symmetric domains Tikhonov method Tikhonov regularization method Time fractional diffusion equation
ISSN号	03770427
DOI	10.1016/j.cam.2020.112998
英文摘要	In this paper, we identify the initial value for a time-fractional diffusion equation on a columnar axis-symmetric domain. This problem is ill-posed, i.e., the solution (if it exists) does not depend continuously on the domain. Two different kinds of fractional Tikhonov methods are used to solve this problem. Under the a priori and the a posteriori regularization parameter choice rules, the error estimates between the regularization solutions and the exact solution are obtained, respectively. Different numerical examples are presented to illustrate the validity and effectiveness of our methods. © 2020 Elsevier B.V.
WOS研究方向	Mathematics
语种	英语
出版者	Elsevier B.V., Netherlands
WOS记录号	WOS:000540354500026
内容类型	期刊论文
源URL	[http://ir.lut.edu.cn/handle/2XXMBERH/150850]
专题	理学院
作者单位	School of Science, Lanzhou University of Technology, Lanzhou, Gansu; 730050, China
推荐引用方式 GB/T 7714	Yang, Fan,Pu, Qu,Li, Xiao-Xiao. The fractional Tikhonov regularization methods for identifying the initial value problem for a time-fractional diffusion equation[J]. Journal of Computational and Applied Mathematics,2020,380.
APA	Yang, Fan,Pu, Qu,&Li, Xiao-Xiao.(2020).The fractional Tikhonov regularization methods for identifying the initial value problem for a time-fractional diffusion equation.Journal of Computational and Applied Mathematics,380.
MLA	Yang, Fan,et al."The fractional Tikhonov regularization methods for identifying the initial value problem for a time-fractional diffusion equation".Journal of Computational and Applied Mathematics 380(2020).