Journal ArticleDOI
Homotopy perturbation method: a new nonlinear analytical technique
TLDR
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.About:
This article is published in Applied Mathematics and Computation.The article was published on 2003-02-01. It has received 1483 citations till now. The article focuses on the topics: Homotopy analysis method & Poincaré–Lindstedt method.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
The application of He's homotopy perturbation method to nonlinear equations arising in heat transfer
TL;DR: In this paper, homotopy perturbation method (HPM), which does not need small parameters in the equations, is compared with the perturbations and numerical methods in the heat transfer field.
Journal ArticleDOI
Modified homotopy perturbation method: Application to quadratic Riccati differential equation of fractional order
Zaid Odibat,Shaher Momani +1 more
TL;DR: In this paper, a modification of He's homotopy perturbation method is presented, which extends the application of the method to solve nonlinear differential equations of fractional order, which does not require a small parameter in an equation.
Journal ArticleDOI
Homotopy perturbation method for nonlinear partial differential equations of fractional order
Shaher Momani,Zaid Odibat +1 more
TL;DR: In this paper, the authors presented an efficient and reliable treatment of the homotopy perturbation method (HPM) for nonlinear partial differential equations with fractional time derivative, described in the Caputo sense.
Journal ArticleDOI
Limit cycle and bifurcation of nonlinear problems
TL;DR: In this paper, a simple but effective iteration method is proposed to search for limit cycles or bifurcation curves of nonlinear equations, and some examples are given to illustrate its convenience and effectiveness.
References
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Journal ArticleDOI
Homotopy perturbation technique
TL;DR: 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.
Journal ArticleDOI
Variational iteration method – a kind of non-linear analytical technique: some examples
TL;DR: In this paper, a variational iteration method for non-linear problems is proposed, where the problems are initially approximated with possible unknowns and a correction functional is constructed by a general Lagrange multiplier, which can be identified optimally via the variational theory.
Journal ArticleDOI
A coupling method of a homotopy technique and a perturbation technique for non-linear problems
TL;DR: In this article, a coupling method of a homotopy technique and a perturbation technique is proposed to solve non-linear problems, which does not require a small parameter in the equation.
Journal ArticleDOI
Approximate analytical solution for seepage flow with fractional derivatives in porous media
TL;DR: In this article, a variational iteration method is used to give approximate solutions of the problem of seepage flow in porous media with fractional derivatives, and the results show that the proposed iteration method, requiring no linearization or small perturbation is very effective and convenient.
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.