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...

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...

In this paper, He’s homotopy perturbation method is applied to solve linear Schrodinger equation. The method yields solutions in convergent series forms with easily computable terms. The result show that these method is very convenient and can be applied to large class of problems. Some numerical examples are given to effectiveness of the method.

In this paper, we apply He’s semi-inverse method to establish a variational theory for the Boussinesq system. Based on this formulation, a solitary solution can be easily obtained using Ritz method. Moreover, the results are also compared with He’s homotopy perturbation method, Liao’s homotopy analysis method and homotopy padémethod. The results reveal that the proposed method is very effective...