A note on the Adomian decomposition method for the generalized Huxley equation

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

doi:10.1016/j.amc.2006.03.011

Cited by 50 publications

(47 citation statements)

References 23 publications

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“…To compute the solutions of the problem, the present work attempts to combine the fourth-order Runge-Kutta (RK4) scheme in time and up to tenth-order FD schemes in space. Numerical computations show that the present methods offer better accuracy in comparison with previous works [7,8].…”

Section: Introductionmentioning

confidence: 70%

“…To show the accuracy of the techniques for the following nonlinear problems in comparison with the exact solution, various error norms are reported at point (x i , t j ). For the computational work, the following examples are taken from [3,7,8,16]. The results are compared with the analytical solutions, and those obtained by other authors using various methods.…”

Section: Numerical Experimentsmentioning

confidence: 97%

“…In the past few years, a great deal of effort has been spent to compute the solution of the Burgers-Huxley equation. Recently various powerful mathematical methods such as spectral methods [3][4][5], Adomian decomposition method [6][7][8], homotopy analysis method [9,10], the tanh-coth method [11], variational iteration method [12,13], Hopf-Cole transformation [14], differential quadrature method [15], meshless method [16] and factorization method [17] have been used in solving the equation.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

High-order finite difference schemes for numerical solutions of the generalized Burgers-Huxley equation

Sarı

Gürarslan

Zeytinoğlu

2010

Numer. Methods Partial Differential Eq.

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In this article, up to tenth-order finite difference schemes are proposed to solve the generalized BurgersHuxley equation. The schemes based on high-order differences are presented using Taylor series expansion. To establish the numerical solutions of the corresponding equation, the high-order schemes in space and a fourth-order Runge-Kutta scheme in time have been combined. Numerical experiments have been conducted to demonstrate the high-order accuracy of the current algorithms with relatively minimal computational effort. The results showed that use of the present approaches in the simulation is very applicable for the solution of the generalized Burgers-Huxley equation. The current results are also seen to be more accurate than some results given in the literature. The proposed algorithms are seen to be very good alternatives to existing approaches for such physical applications.

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Section: Introductionmentioning

confidence: 70%

Section: Numerical Experimentsmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

High-order finite difference schemes for numerical solutions of the generalized Burgers-Huxley equation

Sarı

Gürarslan

Zeytinoğlu

2010

Numer. Methods Partial Differential Eq.

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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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“…For instance, Hashim et al [2] used the Adomian decomposition scheme for the numerical solutions of the generalized Huxley equation. Numerical solutions of the equation was obtained using variational iteration method by Batiha et al [7].…”

Section: Introductionmentioning

confidence: 99%

A New Numerical Scheme for the Generalized Huxley Equation

Inan

2016

BMSA

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Abstract. In this paper, an implicit exponential finite difference method is applied to compute the numerical solutions of the nonlinear generalized Huxley equation. The numerical solutions obtained by the present method are compared with the exact solutions and obtained by other methods to show the efficiency of the method. The comparisons showed that proposed scheme is reliable, precise and convenient alternative method for solution of the generalized Huxley equation.

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A note on the Adomian decomposition method for the generalized Huxley equation

Cited by 50 publications

References 23 publications

High-order finite difference schemes for numerical solutions of the generalized Burgers-Huxley equation

High-order finite difference schemes for numerical solutions of the generalized Burgers-Huxley equation

Application of spectral collocation method to a class of nonlinear PDEs

A New Numerical Scheme for the Generalized Huxley Equation

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