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

By Yasir Khan, Qingbiao Wu. Computers and Mathematics with Applications, 2011

364 citations recorded by the source corpus.

In this paper, a combined form of the Laplace transform method with the homotopy perturbation method is proposed to solve nonlinear equations. This method is called the homotopy perturbation transform method (HPTM). The nonlinear terms can be easily handled by the use of He's polynomials. The proposed scheme finds the solution without any discretization or restrictive assumptions and avoids the round-off errors. The fact that the proposed technique solves nonlinear problems without using Adomian's polynomials can be considered as a clear advantage of this algorithm over the decomposition method.

Subfields: Modeling and Simulation, Numerical Analysis, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/f3fc9412ca4205f0d46c1f4e77e08ddd0bad58ee

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Citations in the corpus

Homotopy Perturbation Sumudu Transform Method for Nonlinear Equations (2011, methodology): “Furthermore, the homotopy perturbation method is also combined with the well-known Laplace transformation method [35, 45] and the variational iteration method [46] to produce a highly effective technique for handling many nonlinear problems.”
Analysis of time-fractional hunter-saxton equation: a model of neumatic liquid crystal (2016, methodology): “The variational iteration method by Cheng [9], the Laplace perturbation method by Khan [10], the Adomian decomposition method [11] and the homotopy decomposition method [12, 13] and many others [14–16].”
A Tutorial Review on Fractal Spacetime and Fractional Calculus (2014, neutral): “The names for the modification of the homotopy perturbation method include 1) Laplace homotopy perturbation method [114], 2) homotopy perturbation transform method [83, 115], 3) He-Laplace method [116], 4) A coupled method of homotopy perturbation method and Laplace transform and others.”
Homotopy Analysis Sumudu Transform Method for Nonlinear Equations (2012, methodology): “[3,6,7,11,14,18,40], homotopy analysis method (HAM) [6,7,12,23,25,26,27,28,29,33], variational iteration method (VIM) [6,7,15,16,17,19], Laplace decomposition method (LDM) [20,24,37,41], homotopy perturbation transform method (HPTM) [22], homotopy perturbation sumudu transform method (HPSTM) [34] an”
Recent developments of some asymptotic methods and their applications for nonlinear vibration equations in engineering problems: a review (2012, neutral): “Elementary introduction and interpretation of the 209 method are given in the following publications [5, 9, 24, 27–33, 59, 63, 64, 68, 84, 91, 93, 95, 210 96, 98, 101, 102, 123, 148, 168, 174, 176, 208, 218].”