In recent years, numerous approaches have been applied for finding the solutions of functional equations. One of them is the optimal homotopy asymptotic method. In current paper, this method has been applied for obtaining the approximate solution of Fisher equation. The reliability of the method will be shown by solving some examples of various kinds and comparing the obtained outcomes with the ...

this paper presents the high order frequency-amplitude relationship for nonlinear transversely vibrating beams with odd and even nonlinearities using homotopy perturbation method with an auxiliary term (hpmat). the governing equations of vibrating buckled beam, beam carrying an intermediate lumped mass and quintic nonlinear beam are investigated to exhibit the reliability and ability of the pro...

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 in bo...

in this paper, we present an ecient numerical algorithm for solving fuzzy systemsof linear equations based on homotopy perturbation method. the method is discussed indetail and illustrated by solving some numerical examples.

In this paper the Bagley-Torvik equation as a prototype fractional differential equation with two derivatives is investigated by means of homotopy perturbation method. The results reveal that the present method is very effective and accurate.

In this paper, we present an efficient numerical algorithm for solving fuzzy systems of linear equations based on homotopy perturbation method. The method is discussed in detail and illustrated by solving some numerical examples.

In this paper, we present homotopy perturbation method (HPM) for solving the Korteweg-de Vries (KdV) equation and convergence study of homotopy perturbation method for nonlinear partial differential equation. We compared our solution with the exact solution and homotopy analysis method (HAM). The results show that the HPM is an appropriate method for solving nonlinear equation.

In this work, we have applied Elzaki transform and He's homotopy perturbation method to solvepartial dierential equation (PDEs) with time-fractional derivative. With help He's homotopy per-turbation, we can handle the nonlinear terms. Further, we have applied this suggested He's homotopyperturbation method in order to reformulate initial value problem. Some illustrative examples aregiven in ord...

In this paper, the solution of the evolutionaryfourth-order in space, Sivashinsky equation is obtained by meansof homotopy perturbation method (textbf{HPM}). The results revealthat the method is very effective, convenient  and quite accurateto systems of nonlinear partial differential equations.

We explain the essence of perturbation problems. The key to understanding is the structure of chain homotopy equivalence – the standard one must be replaced by a finer notion which we call a strong chain homotopy equivalence. We formulate an Ideal Perturbation Lemma and show how both new and classical (including the Basic Perturbation Lemma) results follow from this ideal statement.