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 ¼ 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.

Comparison of solutions of linear and non-linear shallow water wave equations using homotopy perturbation method

“…In this respect, HPM was used by Chen and An (2008) to find the solution of a type of nonlinear coupled equations with parameters derivative, Hemeda (2012) for finding the solution of nonlinear coupled equations and Maturi (2012) to obtain solution of coupled Korteweg-de Vries (KdV) equation, respectively. HPM has also been used by Gupta et al (2012) to solve inverse heat problem and Zhou and Wu (2014) to approximate the solution of Helmholtz equation with space fractional derivatives.…”

Modeling and Analysis of Unsteady Axisymmetric Squeezing Fluid Flow through Porous Medium Channel with Slip Boundary

“…In fluid dynamics, Siddiqui et al [ 35 , 36 ] applied this technique for solving non-linear boundary value problems arising in Newtonian and non-Newtonian fluids. In addition, Zhou and Wu [ 37 ] used this technique in an inverse heat problem. Also, Hamid et al [ 38 ] compared the method with other analytical and numerical techniques, while solving higher order non-linear differential equations.…”

Natural convection of non-Newtonian nanofluid flow between two vertical parallel plates

“…This paper aims to investigate the natural convection of non-Newtonian nanofluid flow between two vertical plates using HPM proposed by He (1999) and Galerkin’s method (Bhat and Chakraverty, 2004; Gerald, 2004). HPM has been used by different authors such as Zhou and Wu (2014), to solve inverse heat problem and recently by Karunakar and Chakraverty (2017), for solving one dimension shallow water wave equation. Kargar and Akbarzade (2012) have used HPM to study the natural convection flow of non-Newtonian fluid between two infinite parallel and vertical flat plates.…”