Title: A numerical approach for solving an inverse parabolic problem with unknown control function

Authors: Reza Pourgholi; Morteza Abtahi; S. Hashem Tabasi

Addresses: School of Mathematics and Computer Sciences, Damghan University, P.O. Box 36715-364, Damghan, Iran ' School of Mathematics and Computer Sciences, Damghan University, P.O. Box 36715-364, Damghan, Iran ' School of Mathematics and Computer Sciences, Damghan University, P.O. Box 36715-364, Damghan, Iran

Abstract: In this paper, we will first study the existence and uniqueness of the solution for a one dimensional inverse heat conduction problem (IHCP) via an auxiliary problem. Then the present work is motivated by desire to obtain numerical approach for solving this IHCP. Our method begins with the utilisation of some transformations. These transformations allow us to eliminate an unknown term from parabolic equation to obtain an inverse parabolic problem with two unknown boundary conditions. To solve this inverse problem, we use the fundamental solution method. The effectiveness of the algorithm is illustrated by numerical example.

Keywords: inverse heat conduction; stability; fundamental solution method; Tikhonov regularisation method; L-curve method; inverse parabolic problem; unknown control function; unknown boundary conditions.

DOI: 10.1504/IJCSE.2015.070994

International Journal of Computational Science and Engineering, 2015 Vol.10 No.4, pp.395 - 401

Received: 24 Apr 2012
Accepted: 21 Aug 2012
Published online: 05 Aug 2015 *

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