A modified fractional Landweber method for a backward problem for the inhomogeneous time-fractional diffusion equation in a cylinder. Issue 11 (1st November 2020)

• Record Type: Journal Article
• Authors: Yang, Shuping; Xiong, Xiangtuan; Han, Yaozong
• Is Part Of: International journal of computer mathematics. Volume 97:Issue 11(2020)
• Page Start: 2375
• Page End: 2393
• Publication Date: 2020-11-01
• Subjects: Backward problem -- modified fractional Landweber method -- error estimate; 35R25 -- 35R30 -- 65J20 -- 65M30; Computers -- Periodicals; Numerical analysis -- Periodicals; Automation -- Periodicals; 004.0151
• DOI: 10.1080/00207160.2020.1803297
• Languages: English
• ISSNs: 0020-7160

Abstract

Abstract : In this paper, we consider a backward problem for the inhomogeneous time-fractional diffusion equation in a cylinder. Such a problem is ill-posed. Based on the solution given by the separation of variables, we apply a modified fractional Landweber method to solve it. Error estimates are presented under the a-priori and the a-posteriori choice rules for regularization parameters, respectively. Relative to the classical Landweber method, the modified fractional Landweber method can reduce the total number of iterations to achieve the same accuracy. Numerical example is given to show the validity of the scheme.