In this work, we consider two-dimensional linear and nonlinear Fredholm integral equations of the first kind. The combination of the regularization method and the homotopy perturbation method, or shortly, the regularization-homotopy method is used to find a solution to the equation. The application of this method is based upon converting the first kind of equation to the second kind by applying...

We suggest and analyze a technique by combining the variational iteration method and the homotopy perturbation method. This method is called the variational homotopy perturbation method. We use this method for solving Generalized Time-space Fractional Schrödinger equation. The fractional derivative is described in Caputo sense. The proposed scheme finds the solution without any discritization, ...

in oil industry, spontaneous imbibition is an important phenomenon in recovery from fractured reservoirs which can be defined as spontaneous uptake of a wetting fluid into a porous solid. spontaneous imbibition involves both cocurrent and countercurrent flows. when a matrix block is partially covered by water, oil recovery is dominated by cocurrent imbibition i.e. the production of non wetting ...

Paper the Jeffery-Hamel flow-a nonlinear equation of 3rd order-is studied by homotopy perturbation method. After introducing homotopy perturbation method and the way of obtaining Adomian’s polynomial, we solved the problem for divergent and convergent channel. Finally, velocity distribution and shear stress constant is depicted at various Reynolds numbers and comparing our results with some ear...

In this paper, Homotopy Analysis Method is used to analyze free non-linear vibrations of a beam simply supported by pinned ends under axial force. Mid-plane stretching is also considered for dynamic equation extracted for the beam. Galerkin decomposition technique is used to transform a partial dimensionless nonlinear differential equation of dynamic motion into an ordinary nonlinear differenti...

Nonlinear differential equations arise in a wide variety of problems such as fluid dynamics, quantum field theory, and plasma physics to describe the various phenomena. These problems, a limited number of them apart, do not have a precise analytical solution, so these nonlinear equations should be solved using approximate methods. The homotopy perturbation method (HPM), first proposed by He in ...

This paper investigates an initial-boundary value problem with nonlocal condition for the wave equation. The numerical solution is developed by using Homotopy perturbation method. This method is based on the use of traditional perturbation method and homotopy technique. Using this method, a rapid convergent series solution can be obtained in most cases. Furthermore, this method does not require...