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Application of the homotopy perturbation method to an inverse heat problem

Application of the homotopy perturbation method to an inverse heat problem Purpose – The purpose of this paper is to present a general framework of Homotopy perturbation method (HPM) for analytic inverse heat source problems. Design/methodology/approach – The proposed numerical technique is based on HPM to determine a heat source in the parabolic heat equation using the usual conditions. Then this shows the pertinent features of the technique in inverse problems. Findings – Using this HPM, a rapid convergent sequence which tends to the exact solution of the problem can be obtained. And the HPM does not require the discretization of the inverse problems. So HPM is a powerful and efficient technique in finding exact and approximate solutions without dispersing the inverse problems. Originality/value – The essential idea of this method is to introduce a homotopy parameter p which takes values from 0 to 1. When p =0, the system of equations usually reduces to a sufficiently simplified form, which normally admits a rather simple solution. As p is gradually increased to 1, the system goes through a sequence of deformations, the solution for each of which is close to that at the previous stage of deformation. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal of Numerical Methods for Heat and Fluid Flow Emerald Publishing

Application of the homotopy perturbation method to an inverse heat problem

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References (31)

Publisher
Emerald Publishing
Copyright
Copyright © 2014 Emerald Group Publishing Limited. All rights reserved.
ISSN
0961-5539
DOI
10.1108/HFF-01-2013-0021
Publisher site
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Abstract

Purpose – The purpose of this paper is to present a general framework of Homotopy perturbation method (HPM) for analytic inverse heat source problems. Design/methodology/approach – The proposed numerical technique is based on HPM to determine a heat source in the parabolic heat equation using the usual conditions. Then this shows the pertinent features of the technique in inverse problems. Findings – Using this HPM, a rapid convergent sequence which tends to the exact solution of the problem can be obtained. And the HPM does not require the discretization of the inverse problems. So HPM is a powerful and efficient technique in finding exact and approximate solutions without dispersing the inverse problems. Originality/value – The essential idea of this method is to introduce a homotopy parameter p which takes values from 0 to 1. When p =0, the system of equations usually reduces to a sufficiently simplified form, which normally admits a rather simple solution. As p is gradually increased to 1, the system goes through a sequence of deformations, the solution for each of which is close to that at the previous stage of deformation.

Journal

International Journal of Numerical Methods for Heat and Fluid Flow – Emerald Publishing

Published: Jul 29, 2014

Keywords: Inverse problem; Homotopy perturbation method; Heat equation; Unknown source term

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