A new a posteriori parameter choice strategy for the convolution regularization of the space-fractional backward diffusion problem

• Cong Shi ^[1] ; Chen Wang ^[1] ; Guanghui Zheng ^[1] ; Ting Wei ^[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. 233-248
• Idioma: inglés
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• Resumen

  • In this paper, we consider a backward space-fractional diffusion problem. We propose an a posteriori parameter choice rule for the regularization method given in Zheng and Wei (2010), where the authors proposed a regularization method called convolution regularization method, and gave an a priori parameter choice strategy. In this paper, we study the same problem but give a new a posteriori parameter choice based on a modified version of the discrepancy principle, and obtain a loglog-type error estimate under an additional source condition. Numerical results show that our method is feasible.