On Homotopy Perturbation and Variational Iteration Methods for Linear and Nonlinear Heat Transfer Equations

Abstract

The traditional perturbation methods depend on a small parameter which is difficult to be found for real-life nonlinear and linear problems. To overcome this shortcoming, two new powerful analytical methods are introduced to solve heat transfer problems in this work. One is He's variational iteration method (VIM) and the other is He's homotopy-perturbation method (HPM). VIM is to construct correction functionals using general Lagrange multipliers identified optimally via the variational theory, and the initial approximations can be freely chosen with unknown constants. HPM deforms a difficult problem into a simple problem which can be easily solved. In this work, we use HPM and VIM to solve linear and nonlinear parabolic equation with variable parameters, which are functions on time and space. This type of equation governs on numerous scientific and engineering problems.