Journal ArticleDOI
Homotopy perturbation technique
TLDR
In this paper, the homotopy perturbation technique does not depend upon a small parameter in the equation and can be obtained uniformly valid not only for small parameters, but also for very large parameters.About:
This article is published in Computer Methods in Applied Mechanics and Engineering.The article was published on 1999-08-01. It has received 3058 citations till now. The article focuses on the topics: Homotopy analysis method & n-connected.read more
Citations
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Journal ArticleDOI
Some asymptotic methods for strongly nonlinear equations
TL;DR: In this paper, a survey of recent developments in asymptotic techniques, which are valid not only for weakly nonlinear equations, but also for strongly ones, is presented.
Journal ArticleDOI
Homotopy perturbation method: a new nonlinear analytical technique
TL;DR: The result reveals that the first order of approximation obtained by the proposed method is valid uniformly even for very large parameter, and is more accurate than the perturbation solutions.
Journal ArticleDOI
Application of homotopy perturbation method to nonlinear wave equations
TL;DR: In this article, the homotopy perturbation method is applied to the search for traveling wave solutions of nonlinear wave equations and some examples are given to illustrate the determination of the periodic solutions or the bifurcation curves of the nonlinear Wave equations.
Journal ArticleDOI
Homotopy Perturbation Method for Bifurcation of Nonlinear Problems
TL;DR: In this article, a simple homotopy is constructed by the modified Lindstedt-Poincare method, by the solution and the coefficient of linear term are expanded into series of the embedding parameter.
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The homotopy perturbation method for nonlinear oscillators with discontinuities
TL;DR: The homotopy perturbation method is applied to the nonlinear oscillators with discontinuities and only one iteration leads to high accuracy of the solutions.
References
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Book
Introduction to perturbation techniques
TL;DR: In this paper, the authors introduce the notion of forced Oscillations of the Duffing Equation and the Mathieu Equation for weakly nonlinear systems with quadratic and cubic nonlinearities.
Journal ArticleDOI
An approximate solution technique not depending on small parameters: A special example
TL;DR: In this paper, a simple non-linear equation is used to describe a kind of analytical technique for nonlinear problems, which is based on both homotopy in topology and the Maclaurin series.
Journal ArticleDOI
Boundary element method for general nonlinear differential operators
TL;DR: In this paper, the basic ideas of homotopy in topology are applied to give a kind of high-order Boundary Element Method (BEM) formulations for strongly nonlinear problems governed by quite general nonlinear differential operators which may not contain any linear operators at all.