In this paper, a combined form of the Laplace transform method with the homotopy perturbation method is proposed to solve nonlinear equations. This method is called the homotopy perturbation transform method (HPTM). The nonlinear terms can be easily handled by the use of He’s polynomials. The proposed scheme finds the solution without any discretization or restrictive assumptions and avoids the...

The aim of this paper is to find the exact solution of nonlinear integro-differential equations using a novel enhanced mo dified homotopy perturbation method. To achieve this goal, we apply the new modified technique and enhance it by separating the known analytic function into two parts. Several examples are provided to present the strength and rapid convergence of proposed method. Some of the...

We investigate the steady two-dimensional flow of a viscous incompressible fluid in a rectangular domain that is bounded by two permeable surfaces. The governing fourth-order nonlinear differential equation is solved by applying the spectral-homotopy analysis method and a novel successive linearisation method. Semianalytical results are obtained and the convergence rate of the solution series w...

We show that recent applications of the homotopy perturbation method the Adomian decomposition method and the variational iteration method are completely useless for the treatment of nonlinear problems.

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 remarkabl...

We comment on the new trend in mathematical physics that consists of obtaining Taylor series for fabricated linear and nonlinear unphysical models by means of homotopy perturbation method (HPM), homotopy analysis method (HAM) and Adomian decomposition method (ADM). As an illustrative example we choose a recent application of the HPM to a dynamic system of anisotropic elasticity.

In this paper, Homotopy perturbation method (HPM) has been applied to investigate the effect of magnetic field on Cu-water nanofluid flow in non-parallel walls. The validity of HPM solutions were verified by comparing with numerical results obtained using a fourth order Runge–Kutta method. Effects of active parameters on flow have been presented graphically. The results show that velocity i...

THE THREE DIMENSIONAL FLOW PAST A STRETCHING SHEET BY EXTENDED OPTIMAL HOMOTOPY ASYMPTOTIC METHOD H. Ullah, S. Islam, M. Idrees, M. Fiza, A. Zaman Abdul Wali Khan University Mardan, 23200, Khyber Pakhtunkhwa, Pakistan ABSTRACT: In this paper Extended Optimal Homotopy Asymptotic Method (EOHAM), a new analytic approximate technique has been used to three dimensional flow past a stretching sheet. ...

The homotopy perturbation method proposed by the present author is further improved in this paper, which is proved to be effective and convenient to solving nonlinear equations. Introduction There exist many difficulties encountered in the application of the traditional perturbation techniques to solving strongly nonlinear equations. Of these, one of the most frustrating is the fact that even a...

In this article Optimal Homotopy Asymptotic Method (OHAM) is used for the solution of homogenous advection equations. The accuracy of the method is analyzed by its comparison with exact and Homotopy Perturbation transforms Method (HPTM) solution. The absolute errors and order of approximation presented.