Application of the homotopy perturbation method to an inverse heat problem

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.

Citation

Zhou, G. and Wu, B. (2014), "Application of the homotopy perturbation method to an inverse heat problem", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 24 No. 6, pp. 1331-1337. https://doi.org/10.1108/HFF-01-2013-0021