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A modified quasi-boundary value method for the backward time-fractional diffusion problem

Published online by Cambridge University Press:  20 January 2014

Ting Wei  and
Jun-Gang Wang
Ting Wei
Affiliation:
School of Mathematics and Statistics, Lanzhou University, P.R. China. tingwei@lzu.edu.cn

Abstract

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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.

Keywords

Backward problemfractional diffusion equationmodified quasi-boundary value methodconvergence analysisa priori parameter choicemorozov’s discrepancy principle

Information

Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 48 , Issue 2: Multiscale problems and techniques , March 2014 , pp. 603 - 621
Copyright
© EDP Sciences, SMAI, 2014

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