Solution of the heat equation in the cast‐mould heterogeneous domain using a weighted algorithm based on the homotopy perturbation method

Abstract

Purpose

The purpose of this paper is to present a weighted algorithm based on the homotopy perturbation method for solving the heat transfer equation in the cast‐mould heterogeneous domain.

Design/methodology/approach

A weighted algorithm based on the homotopy perturbation method is used to minimize the volume of computations. The authors show that this technique yields the analytical solution of the desired problem in the form of a rapidly convergent series with easily computable components.

Findings

The authors illustrate that the proposed method produces satisfactory results with respect to Adomian decomposition method and standard homotopy perturbation method. The reliability of the method and the reduction in the size of computational domain give this method a wider applicability.

Originality/value

This research presents, for the first time, a new modification of the proposed technique, for aforementioned problems and some interesting results are obtained.

Citation

Karimi Vanani, S., Yildirim, A., Soleymani, F., Khan, M. and Tutkun, S. (2013), "Solution of the heat equation in the cast‐mould heterogeneous domain using a weighted algorithm based on the homotopy perturbation method", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 23 No. 3, pp. 451-459. https://doi.org/10.1108/09615531311301245