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Abstract and Applied Analysis
Volume 2014, Article ID 964373, 12 pages
http://dx.doi.org/10.1155/2014/964373
Research Article

A Discretized Tikhonov Regularization Method for a Fractional Backward Heat Conduction Problem

1School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 610054, China
2School of Mathematics, Southwest Jiaotong University, Chengdu 610031, China

Received 30 December 2013; Accepted 7 February 2014; Published 18 March 2014

Academic Editor: Ming Li

Copyright © 2014 Zhi-Liang Deng and Xiao-Mei Yang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We propose a numerical reconstruction method for solving a time-fractional backward heat conduction problem. Based on the idea of reproducing kernel approximation, we reconstruct the unknown initial heat distribution from a finite set of scattered measurements of transient temperature at a fixed final time. The standard Tikhonov regularization technique using the norm of reproducing the kernel Hilbert space as the penalty term is adopted to provide a stable solution when the measurement data contains noise. Numerical results indicate that the proposed method is efficient.