Comparison of homotopy perturbation method and homotopy analysis method

By Ji-Huan He. Applied Mathematics and Computation, 2004

671 citations recorded by the source corpus.

Subfields: Mechanics of Materials, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/e9391e9a065dc7a31d62d05fd5becfe0aa01b239

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In Mechanics of Materials

In Modeling and Simulation

Citations in the corpus

He's homotopy perturbation method for solving systems of Volterra integral equations of the second kind (2009, neutral): “Introduction The Topic of the He’s homotopy perturbation method [1–6] has been rapidly growing in recent years [7–23].”
Approximate general and explicit solutions of nonlinear BBMB equations by Exp-Function method (2009, methodology): “In addition, in recent years, scientists have presented some new methods for solving nonlinear partial differential equations; for instance, Bäcklund transformation method [3], Lie groupmethod [4], Adomian’s decomposition method [5], inverse scattering method [6], Hirota’s bilinear method [7], homot”
Variational Iteration Method for Solving Higher-order Nonlinear Boundary Value Problems Using He's Polynomials (2008, methodology): “The homotopy perturbation method uses the homotopy parameter ρ as an expanding parameter [11-15, 20] to obtain”
Application of He's Homotopy Perturbation Method to Sumudu Transform (2007, methodology): “He [3-6] proposed a new method called homotopy perturbation method (HPM) in 1998.”
Homotopy Perturbation Sumudu Transform Method for Nonlinear Equations (2011, methodology): “He [25-33] developed the homotopy perturbation method (HPM) by merging the standard homotopy and perturbation for solving various physical problems.”
Homotopy perturbation transform method for nonlinear equations using He's polynomials (2011, neutral): “He [25–38] developed the homotopy perturbation method (HPM) by merging the standard homotopy and perturbation for solving various physical problems.”
Couette and Poiseuille Flows for Non-Newtonian Fluids (2006, methodology): “In the present work, we analyze the same problem by the homotopy perturbation method (HPM) proposed recently by He[4-8,10], In one model we use the fourth grade fluid as in [13] and in the other we use Sisko fluid.”