Application on homotopy-perturbation and variational iteration methods for heat equation

The traditional perturbation methods depend on a small parameter which is difficult to be found for real-life nonlinear and linear problems. To overcome address this shortcoming, two new powerful recent 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 used to construct correction functional using general Lagrange multipliers identified optimally via by means of the variational theory, and the initial approximations can be freely arbitrarily chosen with unknown constants. HPM may be used to transform a difficult problem into a simple problem which can be easily solved. In this work, we have used HPM and VIM to solve the heat equations which are functions on time and space. This type of equation governs on numerous scientific and engineering experimentations.