A restrictive Padé approximation for the solution of the generalized Fisher and Burger–Fisher equations

Ismail, Hassan N. A.; Rabboh, Aziza A. Abd

doi:10.1016/s0096-3003(03)00703-3

Cited by 41 publications

(22 citation statements)

References 6 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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“…After finding the DTM solutions, the Padé approximant must be applied. Ismail and Rabboh [28] presented the restrictive Padé approximation for the generalized Fisher and Burger-Fisher equations. The Padé approximants [29] often show superior performance over series approximations and provide a successful tool and promising scheme for identical applications.…”

Section: The Differential Transform Methodsmentioning

confidence: 99%

Analytical modeling of heat convection in magnetized micropolar fluid by using modified differential transform method

Rashidi

Laraqi²,

Parsa

2011

Heat Trans. Asian Res.

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In this study, a new analytical method (DTM-Padé) and the numerical method (by using a fourth-order Runge-Kutta and shooting method) were compared to solve convective heat transfer for a micropolar fluid in the presence of uniform magnetic field. It was shown that the differential transform method (DTM) solutions are only valid for small values of independent variables; therefore the DTM is not applicable for solving magnetohydrodynamic (MHD) boundary-layer equations. The new method (DTM-Padé) has removed this problem. Numerical comparisons between the DTM-Padé and the numerical method revealed that the new method is a powerful method for solving MHD boundary-layer equations. Finally, the analytical and numerical solutions of the problem for different values of the dimensionless parameters are shown simultaneously.

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“…The spatial terms are approximated by the schemes. In order to solve Equation (12), the RK4 scheme is used. Each spatial derivative on the RHS of Equation (12) was computed using the present method and then the semi-discrete equation (12) was solved using the RK4 scheme, through the operations …”

Section: The Fd Schemesmentioning

confidence: 99%

“…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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A restrictive Padé approximation for the solution of the generalized Fisher and Burger–Fisher equations

Cited by 41 publications

References 6 publications

Modified pseudospectral method for generalized Burger's-Fisher equation

Modified pseudospectral method for generalized Burger's-Fisher equation

Analytical modeling of heat convection in magnetized micropolar fluid by using modified differential transform method

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

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