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 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)....

This paper focuses on solving the time fractional Caudrey-Dodd-Gibbon-Sawada-Kotera equation (FCDGSKE). We propose two analytical methods based complex transform, variational iteration method and homotopy perturbation method. The approximated solutions to initial value problems associated with FCDGSKE are provided without linearization complicated calculation. Numerical results show main merits...

By means of He's homotopy perturbation method (HPM) an approximate solution of velocity eld is derived for the ow in straight pipes of non-Newtonian uid obeying the Sisko model. The nonlinear equations governing the ow in pipe are for- mulated and analyzed, using homotopy perturbation method due to He. Furthermore, the obtained solutions for velocity eld is graphically sketched...

The solution methods of nonlinear differential equations are very important because most of the physical phenomena are modelled by using such kind of equations. Therefore, this work presents a rational version of homotopy perturbation method RHPM as a novel tool with high potential to find approximate solutions for nonlinear differential equations. We present two case studies; for the first exa...

This article proposes the application of Laplace Transform-Homotopy Perturbation Method and some of its modifications in order to find analytical approximate solutions for the linear and nonlinear differential equations which arise from some variational problems. As case study we will solve four ordinary differential equations, and we will show that the proposed solutions have good accuracy, ev...

Although homotopy-based methods, namely homotopy analysis method andhomotopy perturbation method, have largely been used to solve functionalequations, there are still serious questions on the convergence issue of thesemethods. Some authors have tried to prove convergence of these methods, butthe researchers in this article indicate that some of those discussions are faulty.Here, after criticizi...

in this paper the bagley-torvik equation as a prototype fractional differential equation with two derivatives is investigated by means of homotopy perturbation method. the results reveal that the present method is very effective and accurate.

The present paper deals with the homotopy perturbation method. The question of whether the homotopy perturbation method is simply the conventional Taylor series expansion is examined. It is proven that under particular choices of the auxiliary parameters the homotopy perturbation method is indeed the Taylor series expansion of the sought solution of nonlinear equations.

Large varieties of physical, chemical, and biological phenomena are governed by nonlinear partial differential equations. Solving nonlinear equations may guide authors to know the described process deeply and sometimes leads them to know some facts that are not simply understood through common observations. The investigation of exact solutions of nonlinear partial differential equations plays a...