In this paper, the homotopy analysis method (HAM) proposed by Liao in 1992 and the homotopy perturbation method (HPM) proposed by He in 1998 are compared through an evolution equation used as the second example in a recent paper by Ganji et al (2007). It is found that the HPM is a special case of the HAM when ~ = −1. However, the HPM solution is divergent for all x and t except t = 0. It is als...

Here, the homotopy analysis method (HAM), which is powerful tool for nonlinear problems, applied to solve the prey and predator problem. The homotopy analysis method contains the auxiliary parameter ¯ h, which provides us with a simple way to adjust and control convergence region of solution series.

To recover a sparse signal from an underdetermined system, we often solve a constrained `1-norm minimization problem. In many cases, the signal sparsity and the recovery performance can be further improved by replacing the `1 norm with a “weighted” `1 norm. Without any prior information about nonzero elements of the signal, the procedure for selecting weights is iterative in nature. Common appr...

In this paper, Elzaki Homotopy Perturbation Method is employed for solving linear and nonlinear differential equations with a variable coffecient. This method is a combination of Elzaki transform and Homotopy Perturbation Method. The aim of using Elzaki transform is to overcome the deficiencies that mainly caused by unsatised conditions in some semi-analytical methods such as Homotopy Perturbat...

In this paper we have used the homotopy analysis method (HAM) to obtain solution of space-time fractional advectiondispersion equation. The fractional derivative is described in the Caputo sense. Some illustrative examples have been presented. The obtained results using homotopy analysis method demonstrate the reliability and efficiency of the proposed algorithm.

solitons are ubiquitous and exist in almost every area from sky to bottom. for solitons to appear, the relevant equation of motion must be nonlinear. in the present study, we deal with the korteweg-devries (kdv), modied korteweg-de vries (mkdv) and regularised longwave (rlw) equations using homotopy perturbation method (hpm). the algorithm makes use of the hpm to determine the initial expansio...

In this paper, a Laplace homotopy analysis method which is based on homotopy analysis method and Laplace transform is applied to obtain the approximate solutions of fractional linear and non-linear differential equations. The proposed algorithm presents a procedure of constructing the set of base functions and gives a high-order deformation equation in simple form. Numerical examples are includ...

In the present study, some perturbation methods are applied to Duffing equations having a displacement time-delayed variable to study the stability of such systems. Two approaches are considered to analyze Duffing oscillator having a strong delayed variable. The homotopy perturbation method is applied through the frequency analysis and nonlinear frequency is formulated as a function of all the ...

In this paper, a theorem is proved which presents the series solution obtained from the homotopy analysis method is convergent to the exact solution of nonlinear age-structured population models.