A New Vision of the He's Homotopy Perturbation Method

Homotopy perturbation transform method for nonlinear equations using He’s polynomials

“…Most of these methods have their inbuilt deficiencies like the calculation of Adomian's polynomials, the Lagrange multiplier, divergent results and huge computational work. He [25][26][27][28][29][30][31][32][33][34][35][36][37][38] developed the homotopy perturbation method (HPM) by merging the standard homotopy and perturbation for solving various physical problems. It is worth mentioning that the HPM is applied without any discretization, restrictive assumption or transformation and is free from round off errors.…”

Homotopy Perturbation Transform Method for Solving Korteweg-DeVries (KDV) Equation

“…In 1992. He [5][6][7][8][9][10][11][12][13][14][15][16][17][18] developed the homotopy perturbation method (HPM) by merging the standard homotopy and perturbation for solving various physical problems. The authors have applied this method successfully to problems arising in mathematics engineering.…”

A Comparative Study of Variational Iteration Method and He-Laplace Method

“…Several techniques including the Adomian decomposition method, the variational iteration method, the weighted finite difference techniques and the Laplace decomposition method have been used to solve nonlinear differential equations [18][19][20][21][22][23][24][25][26]. J. H. He developed the homotopy perturbation method (HPM) [27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42] by merging the standard homotopy and perturbation for solving various physical problems. The Laplace transform is totally incapable of handling nonlinear equations because of the difficulties that are caused by the nonlinear terms.…”