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An iterative method for backward time‐fractional diffusion problem
Author(s) -
Wang JunGang,
Wei Ting
Publication year - 2014
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.21887
Subject(s) - mathematics , a priori and a posteriori , regularization (linguistics) , bounded function , partial differential equation , norm (philosophy) , partial derivative , mathematical optimization , mathematical analysis , computer science , philosophy , epistemology , artificial intelligence , political science , law
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. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 2029–2041, 2014
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