A new modified homotopy perturbation method with two free auxiliary parameters for solving MHD viscous flow due to a shrinking sheet

Abstract

Purpose

The purpose of this paper is to introduce a new version of the homotopy perturbation method (HPM) for solving the magnetohydrodynamic viscous flow due to a shrinking sheet.

Design/methodology/approach

Three terms from HPM solution are used.

Findings

The results show that this method is very effective and simple and can be applied to other nonlinear problems.

Research limitations/implications

Comparison between the HPM and homotopy analysis methods for the studied problem shows a remarkable agreement and reveals that the HPM needs less work.

Practical implications

It is suggested that this method should be called HPM with auxiliary parameters. This paper uses two auxiliary parameters, three or more auxiliary parameters could be used for accuracy consideration.

Originality/value

In this paper, a two‐parameter HPM is applied which is useful for finding an approximate analytical solution of MHD viscous flow due to a shrinking sheet.

Citation

Raftari, B. and Yildirim, A. (2011), "A new modified homotopy perturbation method with two free auxiliary parameters for solving MHD viscous flow due to a shrinking sheet", Engineering Computations, Vol. 28 No. 5, pp. 528-539. https://doi.org/10.1108/02644401111140993