Abstract: In this article, we propose a reliable combination of Homotopy analysis method (HAM) and Laplace decomposition method (LDM) to solve linear and nonlinear partial differential equations effectively with less computation. The proposed method is called homotopy analysis transform method (HATM). This study represents significant features of HATM and its capability of handling linear and n...

In this paper, we consider Adomian Decomposition Method (ADM),and Variational Iteration Method (VIM), Homotopy Analysis Method (HAM), Homotopy Analysis Transform Method (HATM) to solve the FractionalOrder Logistic Equation (FOLE). Comparisons between the approximate analytical solution and exact solution of FOLE are shown. 2010 Mathematics Subject Classication: 34-XX , 34Lxx ,34L30

The homotopy analysis method HAM is applied to obtain the approximate traveling wave solutions of the coupled Whitham-Broer-Kaup WBK equations in shallow water. Comparisons are made between the results of the proposed method and exact solutions. The results show that the homotopy analysis method is an attractive method in solving the systems of nonlinear partial differential equations.

here, a new method called aboodh transform homotopy perturbation method(athpm) is used to solve nonlinear partial dierential equations, we presenta reliable combination of homotopy perturbation method and aboodh transformto investigate some nonlinear partial dierential equations. the nonlinearterms can be handled by the use of homotopy perturbation method. the resultsshow the eciency of this...

Troesch’s problem arose while the investigation of the confinement of a plasma column by applying radiation pressure was being conducted. It is an unstable problem in itself, with a two-point boundary value. The application of the Optimal Homotopy Asymptotic Method (OHAM) is used to attain an approximate solution for the nonlinear differential equation which provides and apt description of Troe...

A scheme is developed for the numerical study of the Korteweg-de Vries (KdV) and the Korteweg-de Vries Burgers (KdVB) equations with initial conditions by a homotopy approach. Numerical solutions obtained by homotopy analysis method are compared with exact solution. The comparison shows that the obtained solutions are in excellent agreement.

The aim of this work is to apply the homotopy perturbation method and homotopy analysis method to the problem of thermal explosion in a flammable gas mixture with the addition of volatile fuel droplets. The system of equations that describes the effects of heating, evaporation, and combustion of fuel in a polydisperse spray is simplified. Both convective and radiative heating of droplets is tak...

0