Optimal error bound and simplified Tikhonov regularization method for a backward problem for the time-fractional diffusion equation

Jun-Gang Wang ^[1] ; Ting Wei ^[1] ; Yu-Bin Zhou ^[1]
1. [1] Lanzhou University
  
  Lanzhou University
  
  China
Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 279, Nº 1 ((1 May 2015)), 2015, págs. 277-292
Idioma: inglés
DOI: 10.1016/j.cam.2014.11.026
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Resumen
- In this paper, we consider a backward problem for a time-fractional diffusion equation. Such a problem is ill-posed. The optimal error bound for the problem under a source condition is analyzed. A simplified Tikhonov regularization method is utilized to solve the problem, and its convergence rates are analyzed under an a priori regularization parameter choice rule and an a posteriori regularization parameter choice rule, respectively. Numerical examples show that the proposed regularization method is effective and stable, and both parameter choice rules work well.