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...

In this paper, we apply the  homotopy analysis method (HAM) for solving fuzzy  linear systems and present  the necessary and sufficient conditions for the convergence of series solution obtained via the HAM. Also, we present a new criterion for choosing a proper value of convergence-control parameter $hbar$ when the HAM is applied to linear system of equations. Comparisons are made between the ...

This article proposes non-linearities distribution Laplace transform-homotopy perturbation method (NDLT-HPM) to find approximate solutions for linear and nonlinear differential equations with finite boundary conditions. We will see that the method is particularly relevant in case of equations with nonhomogeneous non-polynomial terms. Comparing figures between approximate and exact solutions we ...

In this article, we presented a new approach deduced from He’s homotopy perturbation method (HPM) to obtain exact and/or approximate analytical solutions of Emden–Fowler type equations. The results reveal that the proposed algorithm is very effective and in most cases yield exact solutions in the first approximation. Some examples are given to illustrate the new approach.

In this paper, we consider the homotopy perturbation method (HPM) to obtain the exact solution of Hirota-Satsuma Coupled KdV equation. The results reveal that the proposed method is very effective and simple and can be applied to other nonlinear mathematical problems.

An analytic technique, the homotopy analysis method (HAM), is applied to obtain the approximate analytical solutions of fourth-order integro-differential equations. The homotopy analysis method (HAM) is one of the most effective method to obtain the exact and approximate solution and provides us with a new way to obtain series solutions of such problems. HAM contains the auxiliary parameter ħ, ...

Abstract Modeling of the electrostatic potential for fully depleted (FD) silicon-on-insulator (SOI) metal-oxide-semiconductor field effect transistor (MOSFET) is presented in this article. The modeling based on analytical solution two-dimensional Poisson’s equation obtained by using homotopy perturbation method (HPM). HPM with suitable boundary conditions results so-called general and closed-fo...

Simply supported steel beams with rectangular hollow section (RHS) are investigated, taking into account large twist and cross-sections distortions. A closed-form expression for the critical value of external couple inducing lateral torsional buckling is found; homotopy perturbation method (HPM) used to investigate post-buckling non-linear path. The linear paths given by HPM compared those of: ...

In this article New Iterative Method (NIM) is tested upon time fractional coupled ITO system. The results obtained by the proposed method are compared with that of Homotopy Perturbation (HPM). It shown accurate for strongly nonlinear system PDEs.

By means of He's homotopy perturbation method (HPM) an approximate solution of velocity eld is derived for the ow in straight pipes of non-Newtonian uid obeying the Sisko model. The nonlinear equations governing the ow in pipe are for- mulated and analyzed, using homotopy perturbation method due to He. Furthermore, the obtained solutions for velocity eld is graphically sketched...