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...

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 ...

This study proposes and explores a prey–predator model that presents functional response to group behavior of harvesting. We non-linear growths in two species. The proposed is supported by theoretical numerical results. Some descriptions are provided help our analytical conclusions. For all possible parameter values occurring system, we solved it using both VIM (variational iteration method) HP...

0. Introduction A number of mathematical techniques have been applied for solving nonlinear problems. Energy Balance [1–3], homotopy analysis [4], variational iteration [5], homotopy perturbation [6,7], the max–min approach [8,9], frequency amplitude formulation [10] and perturbation methods [11] are the most prominent approaches that those have been employed for solving a large number of nonli...

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...