Abstract: In this study, the problem of laminar, isothermal, incompressible and viscous flow in a rectangular domain bounded by two moving porous walls, which enable the fluid to enter or exit during successive expansions or contractions, is solved using a series of based analytical techniques named Homotopy Perturbation Method (HPM), Differential Transformation Method (DTM) and Optimal Homotop...

In recent years, it has been found that derivatives of non-integer order are very effective for the description of many physical phenomena such as rheology, damping laws, and diffusion processes. These findings invoked the growing interest on studies of the fractal calculus in various fields such as physics, chemistry, and engineering [1 – 4]. In general, there exists no method that yields an e...

in this paper, we give an analytical approximate solution for an integro- differential equation which describes the charged particle motion for certain configurations of oscillating magnetic fields is considered. the homotopy analysis method (ham) is used for solving this equation. several examples are given to reconfirm the efficiency of these algorithms. the results of applying this procedure...

In this communication, we describe the Homotopy Perturbation Method with Laplace Transform (LT-HPM), which is used to solve the Lane-Emden type differential equations. It's very difficult to solve numerically the Lane-Emden types of the differential equation. Here we implemented this method for two linear homogeneous, two linear nonhomogeneous, and four nonlinear homogeneous Lane-Emden type dif...

I discuss a recent application of homotopy perturbation method to a heat transfer problem. I show that the authors make infinity equal five and analyze the consequences of that magic. There has recently been great interest in the application of several approximate procedures, like the homotopy perturbation method (HPM), the Adomian decomposition method (ADM), and the variation iteration method ...

This paper proposes a new technique to solve n-th order linear uncertain but bounded (interval) differential equations with interval initial conditions using the interval midpoint. First, the interval differential equation is solved in terms of the interval midpoint. This solution is then used to find the solution of the original interval differential equation. The method is discussed by consid...

In this paper, Elzaki Homotopy Perturbation Method is employed for solving linear and nonlinear differential equations with a variable coffecient. This method is a combination of Elzaki transform and Homotopy Perturbation Method. The aim of using Elzaki transform is to overcome the deficiencies that mainly caused by unsatised conditions in some semi-analytical methods such as Homotopy Perturbat...

The homotopy perturbation method is a powerful device for solving a wide variety of problems arising in many scientific applications. In this paper, we investigate several integral equations by using T-stability of the Homotopy perturbation method investigates for solving integral equations. Some illustrative examples are presented to show that the Homotopy perturbation method is T-stable for s...

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...

thermal recovery involves well-known processes such as steam injection (cyclic steam stimulation, steam drive, and steam-assisted gravity drainage), in situ combustion, and a more recent technique that consists of heating the reservoir with electrical energy. when high frequency is used for heating, it is called electromagnetic (em) heating. the applications of em heating for heavy-oil reservoi...