Boundary value problems | |
Landweber iterative method for identifying a space-dependent source for the time-fractional diffusion equation | |
Dun-Gang Li1  Yu-Peng Ren1  Fan Yang1  Xiao-Xiao Li1  | |
[1] School of Science, Lanzhou University of Technology, Lanzhou, P.R. China | |
关键词: time-fractional diffusion equation; ill-posed problem; unknown source; Landweber iterative method; 35R25; 47A52; 35R30; | |
DOI : 10.1186/s13661-017-0898-2 | |
学科分类:数学(综合) | |
来源: SpringerOpen | |
【 摘 要 】
This paper is devoted to identifying an unknown source for a time-fractional diffusion equation with variable coefficients in a general bounded domain. This is an ill-posed problem. Firstly, we obtain a regularization solution by the Landweber iterative regularization method. The convergence estimates between regularization solution and exact solution are given under a priori and a posteriori regularization parameter choice rules, respectively. The convergence estimates we obtain are optimal order for any p in two parameter choice rules, i.e., it does not appear to be a saturating phenomenon. Finally, the numerical examples in the one-dimensional and two-dimensional cases show our method is feasible and effective.
【 授权许可】
CC BY
【 预 览 】
Files | Size | Format | View |
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RO201901228799677ZK.pdf | 2173KB | download |