Numerical simulation of the generalized Huxley equation by He’s homotopy perturbation method

Hashemi, Soheila; Daniali, Hamid Reza Mohammadi; Ganji, D.D.

doi:10.1016/j.amc.2007.02.128

Cited by 28 publications

(19 citation statements)

References 12 publications

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“…(6) and (28), and the approximate analytical periodic solutions u EBM (t) computed by Eqs. (6) and (25) are plotted in Figs. 2(a)-(d).…”

Section: Dϕ(28)mentioning

confidence: 99%

“…The traditional perturbation methods have many shortcomings, and they are not valid for strongly nonlinear equations. To overcome the shortcomings, many new techniques have been appeared in open literature [3][4][5][6][7][8][9][10][11][12][13][14], such as Nonperturbative methods [3], homotopy perturbation method [4][5][6][7][33][34][35], perturbation techniques [8], Lindstedt-Poincaré method [9,10], parameter-expansion method [11,12] and Parameterized perturbation method [13,14].…”

Section: Introductionmentioning

confidence: 99%

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Approximate Analytical Solutions to Nonlinear Oscillations of Non-Natural Systems Using He's Energy Balance Method

Ganji¹,

Karimpour²,

Ganji³

2008

PIER M

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Abstract-This paper applies He's Energy balance method (EBM) to study periodic solutions of strongly nonlinear systems such as nonlinear vibrations and oscillations. The method is applied to two nonlinear differential equations. Some examples are given to illustrate the effectiveness and convenience of the method. The results are compared with exact solutions which lead us showing a good accuracy. The method can be easily extended to other nonlinear systems and can therefore be found widely applicable in engineering and other science.

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“…(6) and (28), and the approximate analytical periodic solutions u EBM (t) computed by Eqs. (6) and (25) are plotted in Figs. 2(a)-(d).…”

Section: Dϕ(28)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Approximate Analytical Solutions to Nonlinear Oscillations of Non-Natural Systems Using He's Energy Balance Method

Ganji¹,

Karimpour²,

Ganji³

2008

PIER M

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“…Table 3 for the parameters β = 1, δ = 1, 2, 3 and γ = 0.001. [5,6] applied to same equation with the same parameters β = 1, γ = 0.001 and δ = 1 and consider h t = 10 −4 and N = 10. Table 5 for α = 0, β = 1, γ = 0.001 and α = 0.001, β = 0.001, γ = 0.001.…”

Section: Numerical Examplesmentioning

confidence: 99%

Application of spectral collocation method to a class of nonlinear PDEs

Zarebnia¹,

Jalili²

2013

Communications in Numerical Analysis

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In this paper approximate solutions to a class of nonlinear partial differential equations by means of the Chebyshev spectral collocation method is considered. First, properties of the Chebyshev spectral collocation method required for our subsequent development are given and utilized to reduce the computation of Fisher's, generalized Burger's-Fisher, generalized Huxley, and generalized Burger's-Huxley equations to some system of ordinary differential equations. Then, we use fourth-order Runge-Kutta formula for the numerical solution of the system of ordinary differential equations. The method is applied to a few test examples to illustrate the accuracy and the implementation of the method.

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“…So these nonlinear simultaneous equations should be solved using other methods, namely, numerical or semiexact analytical methods. Some others believe that the combination of numerical and semiexact analytical methods can also produce useful results (Hashemi et al, 2007;Varedi et al, 2009). Choi et al solved forward kinematic problem of H4 and showed that the problem lead to a 16th degree polynomial in a single variable (Choi et al, 2003).…”

Section: Forward Kinematicsmentioning

confidence: 99%