The aim of this work is to apply the homotopy perturbation method and homotopy analysis method to the problem of thermal explosion in a flammable gas mixture with the addition of volatile fuel droplets. The system of equations that describes the effects of heating, evaporation, and combustion of fuel in a polydisperse spray is simplified. Both convective and radiative heating of droplets is tak...

in this paper, an application of homotopy perturbation method is appliedto nding the solutions of the seven-order sawada-kotera (ssk) and a lax'sseven-order kdv (lskdv) equations. then obtain the exact solitary-wave so-lutions and numerical solutions of the ssk and lskdv equations for the initialconditions. the numerical solutions are compared with the known analyticalsolutions. their rem...

In the paper, we discuss applications of Homotopy Perturbation Method (HPM) related to wave equations subjected non-local conditions and method is applied two test problems in paper. The was introduced by J.-H. He (Homotopy perturbation technique, Computer Methods Applied Mechanics Engineering 178(3-4) (1999), 257 – 262) solutions are matched against exact as literature. results indicate that H...

This article involves the study and analysis of fully developed flow a magnetorheological fluid through non-isotropic porous medium under effect an external, uniform, transversal magnetic field. Permeability is taken as exponential distribution function transverse direction. The Darcy-Brinkman-Lapwood-Lorentz equation for in media has been used solved non-slip boundary conditions by Modified Ho...

In this paper, we consider the variational homotopy perturbation method (VHPM) to obtain an approximate series solution for the generalized Fisher’s equation which converges to the exact solution in the region of convergence. Comparisons are made among the variational iteration method (VIM), the exact solutions and the proposed method. The results reveal that the proposed method is very effectiv...

this paper has been devoted to apply the reconstruction of variational iteration method (rvim) to handle the systems of integro-differential equations. rvim has been induced with laplace transform from the variational iteration method (vim) which was developed from the inokuti method. actually, rvim overcome to shortcoming of vim method to determine the lagrange multiplier. so that, rvim method...

This article introduces two well-known computational techniques for solving the time-fractional system of nonlinear equations unsteady flow a polytropic gas. The methods suggested are modified forms variational iteration method and homotopy perturbation by Elzaki transformation. Furthermore, an illustrative scheme is introduced to verify accuracy available techniques. A graphical representation...

Although homotopy-based methods, namely homotopy analysis method and homotopy perturbation method, have largely been used to solve functional equations, there are still serious questions on the convergence issue of these methods. Some authors have tried to prove convergence of these methods, but the researchers in this article indicate that some of those discussions are faulty. Here, after crit...

A new perturbation method called the homotopy perturbation method (HPM) [1 – 4] was proposed by Ji-Huan He in 1999, which is a coupling of the traditional perturbation method and homotopy in topology. The traditional perturbation methods are based on assuming a small parameter, and the approximate solutions obtained by those methods, in most cases, are valid only for small values of the small p...

The solution of the complex neutron diffusion equations system in a spherical nuclear reactor is presented using homotopy perturbation method (HPM); HPM remarkable approximation that successfully solves different systems equations, and this work, solved for first time method. considered consists two consistent subsystems, where studies multi-group subsystem core, other reflector; each can deal ...