Numerical simulation of the generalized Huxley equation by He’s variational iteration method

Batiha, Belal; Noorani, Mohd Salmi Md; Hashim, Ishak

doi:10.1016/j.amc.2006.07.166

Cited by 52 publications

(49 citation statements)

References 9 publications

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“…For this oscillator we have f (x) = x 1/3 and f (x) = 1 3 x −2/3 . The Fourier series expansion of f (A cos ωt) = A 1/3 cos 1/3 ωt is given by (17), where…”

Section: Illustrative Example: Oscillator With Fractional-power Restomentioning

confidence: 99%

Approximate Solutions for Conservative Nonlinear Oscillators by He’s Homotopy Method

Yebra¹

2008

Zeitschrift Für Naturforschung A

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He's homotopy perturbation method is adapted to calculate higher-order approximate periodic solutions of conservative nonlinear oscillators for which the elastic force term is an odd nonlinear function. The method is modified by truncating the infinite series corresponding to the first-order approximate solution before introducing this solution in the second-order linear differential equation, and so on. With carefully constructed iterations, only a few iterations can provide very accurate analytical approximate solutions. An example is presented to illustrate the usefulness and effectiveness of the proposed technique, and comparison of the results obtained using this method with those obtained using other techniques reveals that the former is very effective and convenient.

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“…For this oscillator we have f (x) = x 1/3 and f (x) = 1 3 x −2/3 . The Fourier series expansion of f (A cos ωt) = A 1/3 cos 1/3 ωt is given by (17), where…”

Section: Illustrative Example: Oscillator With Fractional-power Restomentioning

confidence: 99%

Approximate Solutions for Conservative Nonlinear Oscillators by He’s Homotopy Method

Yebra¹

2008

Zeitschrift Für Naturforschung A

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“…It is very difficult to solve nonlinear problems and, in general, it is often more difficult to get an analytic approximation than a numerical one for a given nonlinear problem. There are several methods used to find approximate solutions to nonlinear problems, such as perturbation techniques [1][2][3][4][5][6], harmonic balance based methods [6][7][8][9] or other techniques [10][11][12][13][14][15][16][17][18]. An excellent review on some asymptotic methods for strongly nonlinear equations can be found in detail in references [19] and [20].…”

Section: Introductionmentioning

confidence: 99%

Solution for an anti-symmetric quadratic nonlinear oscillator by a modified He’s homotopy perturbation method

Beléndez

Pascual

Beléndez

et al. 2009

Nonlinear Analysis: Real World Applications

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In this paper He's homotopy perturbation method has been adapted to calculate higherorder approximate periodic solutions of a nonlinear oscillator with discontinuity for which the elastic force term is anti-symmetric and quadratic term. We find He's homotopy perturbation method works very well for the whole range of initial amplitudes, and the excellent agreement of the approximate frequencies and periodic solutions with the exact ones has been demonstrated and discussed. Only one iteration leads to high accuracy of the solutions with a maximal relative error for the approximate period of less than 0.73%for all values of oscillation amplitude, while this relative error is as low as 0.040% when the second iteration is considered. Comparison of the result obtained using this method with those obtained by harmonic balance method reveals that the former is very effective and convenient.

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“…This comparison is benched-marked against a numerical solution. A considerable amount of research work has been conducted recently in applying these methods to a class of linear and nonlinear problems see [10][11][12][13][14]. However, Variational iteration Method has an advantage over Adomian Decomposition Method that it solves nonlinear problems without using Adomian polynomials.…”

Section: Introductionmentioning

confidence: 99%

“…The VIM as a powerful analytical technique was first introduced by He and has been used by many mathematicians to solve various nonlinear equations [10][11][12][13][14]. This method gives rapidly convergent successive approximations of the exact solutions if such solution exists.…”

Section: Introductionmentioning

confidence: 99%

A numerical study of thin film flow of a non-Newtonian fluid on a vertically moving belt using variational iteration approach

Farooq

Batiha²,

Siddiqui³

2013

International Journal of Applied Mathematical Research

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This paper provides an investigation regarding the modeling and analysis of a thin film flow of an Oldroyd 8-constant fluid on a vertically moving belt. The governing nonlinear problem is solved by using Variational Iteration Method (VIM). The results of the present method are then compared with those obtained by Adomian Decomposition Method (ADM) and an excellent agreement is observed. This comparison reveals that VIM may be considered as an efficient alternative method for solving nonlinear problems arising in non-Newtonian fluid mechanics. Expressions for some important physical quantities such as volume flux, average velocity, the belt speed for the lifting of the non-Newtonian fluid are also derived.

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Numerical simulation of the generalized Huxley equation by He’s variational iteration method

Cited by 52 publications

References 9 publications

Approximate Solutions for Conservative Nonlinear Oscillators by He’s Homotopy Method

Approximate Solutions for Conservative Nonlinear Oscillators by He’s Homotopy Method

Solution for an anti-symmetric quadratic nonlinear oscillator by a modified He’s homotopy perturbation method

A numerical study of thin film flow of a non-Newtonian fluid on a vertically moving belt using variational iteration approach

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