Variational iteration method and homotopy perturbation method for nonlinear evolution equations

Ganji, D.D.; Tari, Hafez; Bakhshi-Jooybari, Mohammad

doi:10.1016/j.camwa.2006.12.070

Cited by 94 publications

(65 citation statements)

References 23 publications

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“…If one does not keep this in mind, some useless results might be obtained. For example, let us consider the following linear differential equation [Ganji et al (2007)]:…”

Section: The Perturbation Methodsmentioning

confidence: 99%

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Homotopy Perturbation Method to Solve Heat Conduction Equation

Jawad¹

2012

Heat Transfer Phenomena and Applications

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“…If one does not keep this in mind, some useless results might be obtained. For example, let us consider the following linear differential equation [Ganji et al (2007)]:…”

Section: The Perturbation Methodsmentioning

confidence: 99%

“…Then, regarding p as a small parameter, [Ganji et al (2007)] expanded (,: ) xt p ϕ in a power series…”

Section: The Perturbation Methodsmentioning

confidence: 99%

Homotopy Perturbation Method to Solve Heat Conduction Equation

Jawad¹

2012

Heat Transfer Phenomena and Applications

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“…In Figure 1 we present a variety of comparisons between the approximate and exact solution for Equation (10). For 2 a = , 1 ε = .…”

Section: Example 1: Classical Fractional Van Der Pol Oscillatormentioning

confidence: 99%

“…Recently, several methods have been used to find approximate solutions to nonlinear problems, such as, the homotopy perturbation method [2]- [7], the variational iteration method [8]- [10], and the energy balance method [11]- [14].…”

Section: Introductionmentioning

confidence: 99%

Application of the Homotopy Perturbation Method to Nonlinear Heat Conduction and Fractional Van der Pol Damped Nonlinear Oscillator

Nofel¹

2014

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In this paper, a powerful analytical method, called He's homotopy perturbation method is applied to obtaining the approximate periodic solutions for some nonlinear differential equations in mathematical physics via Van der Pol damped non-linear oscillators and heat transfer. Illustrative examples reveal that this method is very effective and convenient for solving nonlinear differential equations. Comparison of the obtained results with those of the exact solution, reveals that homotopy perturbation method leads to accurate solutions.

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“…An analytical solution or a direct answer is usually difficult to find. Therefore an approximation approaches such as (HPM, HAM and VIM) might be of alternatives [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Homotopy perturbation based linearization of nonlinear heat transfer dynamic

HosseinNia

Ranjbar

Ganji

et al. 2008

J. Appl. Math. Comput.

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In this paper a new linearization procedure based on Homotopy Perturbation Method (HPM) will be presented. The procedure begins with solving nonlinear differential equation by HPM. This will be done by evaluation of the time response of a nonlinear dynamic. An equivalent Laplace transform of the time response will be obtained. In the preceding, the effect of an external excitation i.e. input, will be removed from the model to find an approximate linear model for the nonlinear dynamic. The effectiveness of the procedure is verified using a heat transfer nonlinear equation. Ultimately, both HPM based linear model and that of nonlinear have been controlled via a closed loop PID controller. The simulation result shows the significance of the proposed technique.

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Variational iteration method and homotopy perturbation method for nonlinear evolution equations

Cited by 94 publications

References 23 publications

Homotopy Perturbation Method to Solve Heat Conduction Equation

Homotopy Perturbation Method to Solve Heat Conduction Equation

Application of the Homotopy Perturbation Method to Nonlinear Heat Conduction and Fractional Van der Pol Damped Nonlinear Oscillator

Homotopy perturbation based linearization of nonlinear heat transfer dynamic

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