An Iterative Method for Backward Time-Fractional Diffusion Problem

被引：38

作者：

Wang, Jun-Gang ^{[1
]}

Wei, Ting ^{[1
]}

机构：

[1] Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Peoples R China

来源：

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS | 2014年 / 30卷 / 06期

关键词：

a posteriori parameter choice; a priori parameter choice; backward problem; convergence analysis; fractional diffusion equation; iterative regularization method; REGULARIZATION METHOD; ANOMALOUS TRANSPORT; CAUCHY-PROBLEM; EQUATIONS; CALCULUS;

D O I：

10.1002/num.21887

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The aim of this work is to solve the backward problem for a time-fractional diffusion equation with variable coefficients in a general bounded domain. The problem is ill-posed in L-2 norm sense. An iteration scheme is proposed to obtain a regularized solution. Two kinds of convergence rates are obtained 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. (C) 2014 Wiley Periodicals, Inc.

引用

页码：2029 / 2041

页数：13

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