In this work a nearly new established analytical approach, He’s homotopy-perturbation method (HPM) has been applied to solve the differential equation of oscillator with a high degree of The objective of this paper is to present an analytical investigation to analyze the vibration cubic positive nonlinearity of complex variable in nonlinear dynamic systems. The comparison of the solution obtain...

In this study, we find the exact solution of certain partial differential equations (PDE) by proposing and using the Homo-Separation of Variables method. This novel analytical method is a combination of the homotopy perturbation method (HPM) with the separation of variables method. The exact solutions are constructed by choosing an appropriate initial approximation in addition to only one term ...

In this paper, quadratic nonlinear oscillators under stochastic excitation are considered. The Wiener-Hermite expansion with perturbation (WHEP) method and the homotopy perturbation method (HPM) are used and compared. Different approximation orders are considered and statistical moments are computed in the two methods. The two methods show efficiency in estimating the stochastic response of the...

In the present paper, The homotopy perturbation method (HPM) is applied to obtain approximate analytical solutions of the fractional non-linear Schrodinger equations. The solutions are obtained in the form of rapidly convergent infinite series with easily computable terms. Finally, we have illustrated the ability of the method for solving fractional non linear equation by some examples.

We study kinetic models of reversible enzyme reactions and compare two techniques for analytic approximate solutions of the model. Analytic approximate solutions of non-linear reaction equations for reversible enzyme reactions are calculated using the Homotopy Perturbation Method (HPM) and the Simple Iteration Method (SIM). The results of the approximations are similar. The Matlab programs are ...

In this paper, the fractional Sturm-Liouville problems, in which the second order derivative is replaced by a fractional derivative, are derived by the Homotopy perturbation method. The fractional derivatives are described in the Caputo sense. The present results can be implemented on the numerical solutions of the fractional diffusion-wave equations. Numerical results show that HPM is effectiv...

In this paper, the homotopy perturbation method (HPM) is applied to obtain an approximate solution of the fractional Bratu-type equations. The convergence of the method is also studied. The fractional derivatives are described in the modied Riemann-Liouville sense. The results show that the proposed method is very ecient and convenient and can readily be applied to a large class of fractional p...

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 this paper, the problem of forced convection over a horizontal flat plate under condition of variable plate temperature is presented and the homotopy perturbation method (HPM) is employed to compute an approximation to the solution of the system of nonlinear differential equations governing the problem. This paper provides good supplements to the existing literature and generalizes the previ...

It is well-known that the matrix equations play a significant role in several applications in science and engineering. There are various approaches either direct methods or iterative methods to evaluate the solution of these equations. In this research article, the homotopy perturbation method (HPM) will employ to deduce the approximated solution of the linear matrix equation in the form AXB=C....