Spectral collocation method for the solution of the generalized Burger–Fisher equation

Javidi, Mohammad

doi:10.1016/j.amc.2005.04.084

Cited by 50 publications

(26 citation statements)

References 8 publications

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“…in the point (x i , t j ) where Ψ(x i , t j ) is the solution obtained by equation (29) solved by forth order Runge-Kutta method and Ψ(x i , t j ) is the exact solution.For the computational work we select the following examples from [10,11,12]. In the examples 1-3 we take N = 16, Δt = 0.0001 .…”

Section: Numerical Resultsmentioning

confidence: 99%

Modified pseudospectral method for generalized Burger's-Fisher equation

Javidi¹

2006

imf

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We consider solitary-wave solutions of the generalized Burger's-Fisher equationIn this paper, we present a new method for solving of the generalized Burger's-Fisher equation by using the collocation formula for calculating spectral differentiation matrix for Chebyshev-Gauss-Lobatto point. To reduce round-off error in spectral collocation method we use a new precondotioning. Firstly, theory of application of spectral collocation method on Burger's-Fisher equation presented. This method yields Burger's-Fisher equation to a system of ordinary differential equations(ODEs). Secondly, we use forth order Runge-Kutta formula for the numerical integration of the system of ODE. The numerical results obtained by this way have been compared with the exact solution to show the efficiency of the method. Mathematics Subject Classification: 35Q53

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Section: Numerical Resultsmentioning

confidence: 99%

Modified pseudospectral method for generalized Burger's-Fisher equation

Javidi¹

2006

imf

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“…With the use of Adomian decomposition method, solutions of BurgerHuxley and Burgers-Fisher equations were obtained by Ismail et al [4]. Recently, some various powerful mathematical methods such as tanh function methods [5][6][7], tanh-coth method [8], variational iteration method [9], factorization method [10] and spectral collocation method [11,12] have also been used in attempting to solve the equation.…”

Section: Introductionmentioning

confidence: 98%

A compact finite difference method for the solution of the generalized Burgers–Fisher equation

Sarı

Gürarslan²,

Dağ³

2009

Numerical Methods Partial

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In this article, numerical solutions of the generalized Burgers-Fisher equation are obtained using a compact finite difference method with minimal computational effort. To verify this, a combination of a sixth-order compact finite difference scheme in space and a low-storage third-order total variation diminishing RungeKutta scheme in time have been used. The computed results with the use of this technique have been compared with the exact solution to show the accuracy of it. The approximate solutions to the equation have been computed without transforming the equation and without using linearization. Comparisons indicate that there is a very good agreement between the numerical solutions and the exact solutions in terms of accuracy. The present method is seen to be a very good alternative to some existing techniques for realistic problems.

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“…The Adomian decomposition method was used by Ismail et al [3] in solving Burgers-Huxley and Burgers-Fisher equations. Recently, various methods, such as tanh function methods [4][5][6], tanh-coth method [7], variational iteration method [8], factorization method [9], spectral collocation method [10,11] and finite difference (FD)-based methods [12], have also been used for solving the equation.…”

Section: Introductionmentioning

confidence: 99%

High-order finite difference schemes for the solution of the generalized Burgers-Fisher equation

Sarı

Gürarslan

Zeytinoğlu

2009

Int. J. Numer. Meth. Biomed. Engng.

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SUMMARYUp to tenth-order finite difference (FD) schemes are proposed in this paper to solve the generalized Burgers-Fisher equation. The schemes based on high-order differences are presented using Taylor series expansion. To obtain the solutions, up to tenth-order FD schemes in space and fourth-order Runge-Kutta scheme in time have been combined. Numerical experiments have been conducted to demonstrate the efficiency and high-order accuracy of the present methods. The produced results are also seen to be more accurate than some available results given in the literature. Comparisons showed that there is very good agreement between the numerical solutions and the exact solutions in terms of accuracy. The present methods are seen to be very good alternatives to some existing techniques for such realistic problems.

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Spectral collocation method for the solution of the generalized Burger–Fisher equation

Cited by 50 publications

References 8 publications

Modified pseudospectral method for generalized Burger's-Fisher equation

Modified pseudospectral method for generalized Burger's-Fisher equation

A compact finite difference method for the solution of the generalized Burgers–Fisher equation

High-order finite difference schemes for the solution of the generalized Burgers-Fisher equation

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