[PDF] Top 20 Homotopy Analysis Method for Equations of the Type Δ2=b(x,y) and Δ2u=b(x,y,u)

... The homotopy analysis method is developed in 1992 by Liao ...this method is independent of small/large physical ...This method has been successfully applied to solve many linear and non ... See full document

... The homotopy analysis method (HAM) was proposed by Liao in His works ...this method has been successfully em- ployed to solve many types of linear or non-linear, homogeneous or non- ... See full document

... integral equations arise in many industrial fields, such as: electromagnetic fields and thermal ...integral equations of the second kind and propose a new method to solve them, namely “homotopy ... See full document

... of homotopy analysis method (HAM) and the Aboodh transform method, proved very effective to solve non- linear partial differential ...the homotopy anal- ysis Aboodh transform ... See full document

... Laplace homotopy analysis method (LHAM) to solved linear fractional partial differential equations using fractional operators of Liouville-Caputo and Caputo-Fabrizio ...proposed method ... See full document

... of homotopy analysis method (HAM) and the natural transform method proved very effective to solve nonlinear fractional partial differential ...this method is its ability to combine two ... See full document

... Siddiqi and Iftikhar used the variation of parameter method for solving the seventh-order boundary value problems in [7]. Liu and Wu [6] give the general differential quadrature rule (GDQR) for the solution of ... See full document

... [3] Bataineh A.Sami, Noorani M.S.M. , Hashim I., Modified homotopy analysis method for solving systems of second-order BVPs, Commun. Nonlinear Sci. Numer. Simul., in press ... See full document

... A new modification of the Homotopy Analysis Method (HAM) is presented for highly nonlinear ODEs on a semi-infi- nite domain. The main advantage of the modified HAM is that the number of terms in the ... See full document

... The homotopy analysis method (HAM) was proposed by ...this method, the solution is considered as the summation of an infinite series, which usually converges rapidly to the exact ...on ... See full document

... of homotopy in topology combined with the traditional perturbation method for the solution of non linear equations, but contrary to the traditional perturbation methods, HAM doesn’t need a small ... See full document

... [6] Ahmad El-Ajou, Zaid Odibat , Shaher Momani , Ahmad Alawneh, Construction of Analytical Solutions to Fractional Differential Equations Using Homotopy Analysis Method, IAENG International ... See full document

... differential equations with initial and boundary ...differential equations are of fundamentally significant in science and ...differential equations in physics and mathematics is still a significant ... See full document

... using Homotopy Analysis Method (HAM) and extended to the problem by studying the effects of Prandtl number alongside with pressure ...using Homotopy Analysis Method (HAM) and ... See full document

... the homotopy analysis method to construct the numerical solutions for system of fractional order ordinary linear and non-linear equations in section 3, some examples are given to show the ... See full document

... the homotopy analysis method (HAM) to obtain analytic solutions of the space- and time-fractional Fokker–Planck ...computational method that yields analytical solutions and has certain ... See full document

... The homotopy analysis method has been well applied on the non-linear reaction diffusion system of equations of Lotka- Volterratypefor finding the approximate ...Table B show much ... See full document

... differential equations since they appear in many physical phenomena which in general are very hard to solve ...are homotopy analysis method [3], homotopy perturbation method [4], ... See full document

... differential equations with e Schrodinger equation is one of the im- many applications in physics and ...difference method [16], variational iteration method [17], Adomian decomposition method ... See full document

... decomposition method [1] [2], the homotopy analysis method [3] [4], the variational iteration method [5] [6], the homotopy perturbation method [7]-[10], and variational ... See full document