Simple and accurate approach for solving of nonlinear heat convective-radiative equation in fin by using the collocation method and comparison with HPM and VIM

Abstract

Collocation Method (CM) such as analytical technique, which does not need small parameters is here used to evaluate the analytical approximate solutions of the nonlinear heat transfer equation. The obtained results from Collocation Method are compared with other analytical techniques such as Homotopy Perturbation Method (HPM) and Variation Iteration Method (VIM). Also, boundary value problem (BVP) is applied as a numerical method for validation. The results reveal that the Collocation Method is very effective, simple and more accurate than other techniques. Also, it is found that this method is a powerful mathematical tool and can be applied to a large class of linear and nonlinear problems arising in different fields of science and engineering especially at some heat transfer equations.

Keywords

• heat transfer
• collocation method
• homotopy perturbation method
• variational iteration method