Application of Variational Iteration and Homotopy-Perturbation Methods to Nonlinear Heat Transfer Equations with Variable Coefficients

Abstract

Since analytical perturbation methods depend on a small parameter and finding this small parameter is difficult, two powerful analytical methods are introduced to be applied to solve nonlinear heat transfer problems in this article. One is He's variational iteration method ( VIM ) and the other is the homotopy-perturbation method ( HPM ). The VIM is used to construct correction functionals using general Lagrange multipliers identified optimally via the variational theory. The HPM converts a difficult problem into a simple problem which can be easily solved. In this article, the VIM is used to solve some nonlinear heat transfer equations with variable heat transfer coefficient. The results are then compared with those obtained by the HPM and the exact solution.