A modified quasi-boundary value method for the backward time-fractional diffusion problem. (20th January 2014)

• Record Type: Journal Article
• Authors: Wei, Ting; Wang, Jun-Gang
• Is Part Of: Mathematical modelling and numerical analysis. Volume 48:Part 2(2014)
• Page Start: 603
• Page End: 621
• Publication Date: 2014-01-20
• Subjects: Backward problem, -- fractional diffusion equation, -- modified quasi-boundary value method, -- convergence analysis, -- a priori parameter choice, -- morozov's discrepancy principle; Numerical analysis -- Periodicals; Mathematical models -- Periodicals; 510
• DOI: 10.1051/m2an/2013107
• Languages: English
• ISSNs: 0764-583X

Abstract

Abstract : In this paper, we consider a backward problem for a time-fractional diffusion equation with variable coefficients in a general bounded domain. That is to determine the initial data from a noisy final data. Based on a series expression of the solution, a conditional stability for the initial data is given. Further, we propose a modified quasi-boundary value regularization method to deal with the backward problem and obtain two kinds of convergence rates by using an a priori regularization parameter choice rule and an a posteriori regularization parameter choice rule. Numerical examples in one-dimensional and two-dimensional cases are provided to show the effectiveness of the proposed methods.