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 ...

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.

A numerical solution for solving non-linear Fredholm integral equations is presented. The method is based upon homotopy perturbation theory. The result reveal that the modified homotopy perturbation method (MHPM) is very effective and convenient. 2007 Elsevier Ltd. All rights reserved.

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...