Landweber iterative method for identifying a space-dependent source for the time-fractional diffusion equation

• Main Authors: Fan Yang, Yu-Peng Ren, Xiao-Xiao Li, Dun-Gang Li
• Format: Article
• Language: English
• Published: SpringerOpen 2017-11-01
• Series: Boundary Value Problems
• Subjects: time-fractional diffusion equation; ill-posed problem; unknown source; Landweber iterative method
• Online Access: http://link.springer.com/article/10.1186/s13661-017-0898-2

Abstract 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.