Applications of He's Homotopy Perturbation Method to Obtain Second-order Approximations of the Coupled Two-Degree-of-Freedom Systems

A novel and developed approximation for motion of a spherical solid particle in plane coquette fluid flow

“…One of the recent analytical methods used in the literature, namely, the Homotopy Perturbation Method (HPM) which was firstly proposed by Chinese mathematician Ji-Huan He [1][2][3][4][5][6][7][8] has attracted special attention of researchers as it is flexible in applying and gives sufficiently accurate results with modest effort. This method is a powerful series-based analytical tool that has been used by many authors [9][10][11][12][13][14] however, the convergence region of the obtained truncated series approximation is limited and in the best case scenario, it needs some enhancements to enlarge the convergence region of the approximate solution. It is well known that Padé approximations which was presented by Padé in 1892 [15], have the advantage of manipulating the polynomial approximation into a rational function of polynomials.…”

Analytical investigation of Jeffery-Hamel flow with high magnetic field and nanoparticle by Adomian decomposition method

“…ADM also was used by several researchers to solve a wide range of physical problems in various engineering fields such as fluid flow and porous media simulation [21] and other nonlinear systems [22][23][24][25][26] . In recent years, some researchers used new methods to solve these kinds of problems [27][28][29][30][31][32][33][34][35][36][37][38][39][40] . In this paper, we apply the ADM to find the approximate solutions of nonlinear differential equations governing the MHD Jeffery-Hamel flow, and a comparison between the ADM and mumerical solution results is provided.…”

Solution of the Jeffery–Hamel flow problem by optimal homotopy asymptotic method

“…In recent years, much attention has been devoted to the newly developed methods for constructing an analytic solution of an equation; such methods include the homotopy analysis method (HAM) [12][13][14][15][16][17][18][19], the homotopy perturbation method (HPM) [20][21][22][23][24][25][26], and the variational iteration method (VIM) [27][28][29][30][31][32]. Perturbation techniques are too strongly dependent upon the so-called ''small parameters''.…”