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...

The homotopy perturbation method is extremely accessible to non-mathematicians and engineers. The method decomposes a complex problem under study into a series of simple problems that are easy to be solved. This note gives an elementary introduction to the basic solution procedure of the homotopy perturbation method. Particular attention is paid to constructing a suitable homotopy equation. Thi...

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 ...

In this paper, a comparison among the hybrid of Fourier Transform and AdomianDecomposition Method (FTADM) and Homotopy Perturbation Method (HPM) is investigated.The linear and non-linear Newell-Whitehead-Segel (NWS) equations are solved and the results arecompared with the exact solution. The comparison reveals that for the same number of componentsof recursive sequences, the error of FTADM is ...

Abstract This paper presents the solution of important types non-linear time-fractional partial differential equations via conformable Elzaki transform Homotopy perturbation method. We apply proposed technique to solve four equations. In addition, we establish results on uniqueness and convergence solution. Finally, numerical for a variety α values are briefly examined. The method performs well...

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 paper, the homotopy perturbation method and a modified homotopy perturbation method are used for analytical treatment of the wave equation and some nonlinear diffusion equations, respectively. Some examples are given to illustrate that a suitable choice of an initial solution can lead to the exact solution, this revealing the reliability and effectiveness of the method. © 2009 Elsevier ...

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.