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Mathematical Problems in Engineering
Volume 2015, Article ID 573932, 9 pages
http://dx.doi.org/10.1155/2015/573932
Research Article

Time- or Space-Dependent Coefficient Recovery in Parabolic Partial Differential Equation for Sensor Array in the Biological Computing

1Department of Computer Science, Harbin Institute of Technology at Weihai, Weihai, Shandong 264209, China
2Department of Mathematics, Harbin Institute of Technology, Harbin, Heilongjiang 150001, China
3Beijing Key Laboratory of Mobile Computing & Pervasive Device, Institute of Computing Technology, Beijing, China
4Department of Multimedia, Sungkyul University, Anyō, Gyeonggi 100190, Republic of Korea

Received 3 November 2014; Revised 18 December 2014; Accepted 19 December 2014

Academic Editor: Bo-Wei Chen

Copyright © 2015 Guanglu Zhou et al. 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

This study presents numerical schemes for solving a parabolic partial differential equation with a time- or space-dependent coefficient subject to an extra measurement. Through the extra measurement, the inverse problem is transformed into an equivalent nonlinear equation which is much simpler to handle. By the variational iteration method, we obtain the exact solution and the unknown coefficients. The results of numerical experiments and stable experiments imply that the variational iteration method is very suitable to solve these inverse problems.