In this paper, linear and non-linear stiff systems of ordinary differential equations are solved by the multi-stage homotopy perturbation method (MHPM). The MHPM is a technique adapted from the standard homotopy perturbation method (HPM) where standard HPM is converted into a hybrid numeric-analytic method called multistage homotopy perturbation method (HPM). The MHPM is tested for several exam...

in this study, a new efficient semi-analytical method is introduced to give approximate solutions of strongly nonlinear oscillators. the proposed method is based on combination of two different methods, the multi-step homotopy analysis method and spectral method, called the multi-step spectral homotopy analysis method (msham). in this method, firstly, we propose a new spectral homotopy analysis...

In this paper, homotopy perturbation method is applied to solve moving boundary and isoperimetric problems. This method does not depend upon a small parameter in the equation, homotopy is constructed with an imbedding parameter p, which is considered as a “small parameter”. Finally, we use combined homotopy perturbation method and Green’s function method for solving second order problems. Some ...

The famous Perona-Malik (P-M) equation which was at first introduced for image restoration has been solved via various numerical methods. In this paper we will solve it for the first time via applying a new numerical method called Homotopy Perturbation Method (HMP) and the correspondent approximated solutions will be obtained for the P-M equation with regard to relevant error analysis. Through ...

This paper proposed an efficient modification of homotopy perturbation transform method (HPTM), namely modified homotopy perturbation transform method (MHPTM) for the solution of third order boundary layer equation on semi-infinite domain. The technique was based on the application of Laplace transform to boundary layers in fluid mechanics. The nonlinear terms can be easily handled by the use o...

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. ...

In this study, the implantation of a new semi-analytical method called optimal auxiliary function (OAFM) has been extended to partial differential equations. The adopted was tested upon for approximate solution generalized modified b-equation. first-order numerical obtained by OAFM compared with variational homotopy perturbation (VHPM). possesses and control parameters which can be easily handl...

Fractional differential equations can model various complex problems in physics and engineering, but there is no universal method to solve fractional models precisely. This paper offers a new hope for this purpose by coupling the homotopy perturbation with Aboodh transform. The hybrid technique leads simple approach finding an approximate solution, which converges fast exact one less computing ...

In this paper, we consider the application of the homotopy perturbation method (HPM) to compute the eigenvalues of the Sturm-Liouville problem (SLP) which is called non-definite SLP. Two important Examples show that HPM is reliable method for computing the eigenvalues of SLP.

In this article, the homotopy perturbation method is proposed to solve systems of Volterra integral equations of the first kind. Theoretical proposes are presented briefly, so that this paper can be read independently. To illustrate the method some examples are presented. The results reveal that the homotopy perturbation method is very effective and simple and gives the exact solutions.