A highly accurate method to solve Fisher’s equation

Bastani, Mehdi; Salkuyeh, Davod Khojasteh

doi:10.1007/s12043-011-0243-8

Cited by 42 publications

(49 citation statements)

References 30 publications

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“…In a recent study, Bastani et al considered families of equations of the reaction diffusion type that are similar to Fisher's equation . Such families are described by the equation

\frac{\partial U}{\partial t} = \frac{\partial^{2} U}{\partial x^{2}} + f (U),

where f ( U ) is given by the particular phenomenon to be studied.…”

Section: Results Of the Numerical Simulationmentioning

confidence: 99%

“…In this work, three different numerical experiments were considered to show the advantages of our proposed method. To begin with, a comparison between the explicit Chebyshev Multidomain Pseudospectral (CMD) method used in , the CFD6 method developed by Bastani and the ICMD method developed here, is presented to compare their performance for a fixed number of points and time step τ . Our interest is to see how the solution of ICMD behaves respect to the explicit solution of CMD.…”

Section: Results Of the Numerical Simulationmentioning

confidence: 99%

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An implicit pseudospectral scheme to solve propagating fronts in reaction‐diffusion equations

Olmos‐Liceaga

Segundo-Caballero

2015

Numerical Methods Partial

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Some Reaction‐Diffusion equations present solutions of the traveling wave form. In this work, we present an implicit numerical scheme based on finite difference originally proposed to solve hyperbolic equations. Then, this method is improved using a pseudospectral approach to discretize the spatial variable. The results prove that this new scheme is useful to solve equations of the parabolic type which presents traveling wave solutions. In particular, problems where a reduction in the number of discretization points and an increase of the size of the time step play an important role in their solution are considered. The implicit scheme presented involves the solution of linear systems only. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 86–105, 2016

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“…In a recent study, Bastani et al considered families of equations of the reaction diffusion type that are similar to Fisher's equation . Such families are described by the equation

\frac{\partial U}{\partial t} = \frac{\partial^{2} U}{\partial x^{2}} + f (U),

where f ( U ) is given by the particular phenomenon to be studied.…”

Section: Results Of the Numerical Simulationmentioning

confidence: 99%

Section: Results Of the Numerical Simulationmentioning

confidence: 99%

An implicit pseudospectral scheme to solve propagating fronts in reaction‐diffusion equations

Olmos‐Liceaga

Segundo-Caballero

2015

Numerical Methods Partial

View full text Add to dashboard Cite

show abstract

“…To ensure the accuracy of the proposed numerical techniques, the thermal wave propagating model is solved using presented methods and compared with the available analytical solution [14,20]. Consider a one-dimensional problem of thermal wave propagation along x-direction as: …”

Section: Results and Discussion For One Dimension Analysismentioning

confidence: 99%

The Differential Quadrature Solution of Reaction-Diffusion Equation Using Explicit and Implicit Numerical Schemes

Salah¹,

Amer²,

Matbuly³

2014

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In this paper, two different numerical schemes, namely the Runge-Kutta fourth order method and the implicit Euler method with perturbation method of the second degree, are applied to solve the nonlinear thermal wave in one and two dimensions using the differential quadrature method. The aim of this paper is to make comparison between previous numerical schemes and detect which is more efficient and more accurate by comparing the obtained results with the available analytical ones and computing the computational time.

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“…To ensure the accuracy of the proposed block marching technique, the thermal wave propagating model is solved using presented method and compared with the available analytical solution [15,21] and also compared with the hybrid technique of differential quadrature method and Runge-Kutta fourth order method [15].…”

Section: Resultsmentioning

confidence: 99%

An Efficient Method to Solve Thermal Wave Equation

Salah¹,

Amer²,

Matbuly³

2014

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In this paper, an efficient technique of differential quadrature method and perturbation method is employed to analyze reaction-diffusion problems. An efficient method is presented to solve thermal wave propagation model in one and two dimensions. The proposed method marches in the time direction block by block and there are several time levels in each block. The global method of differential quadrature is applied in each block to discretize both the spatial and temporal derivatives. Furthermore, the proposed method is validated by comparing the obtained results with the available analytical ones and also compared with the hybrid technique of differential quadrature method and Runge-Kutta fourth order method.

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A highly accurate method to solve Fisher’s equation

Cited by 42 publications

References 30 publications

An implicit pseudospectral scheme to solve propagating fronts in reaction‐diffusion equations

An implicit pseudospectral scheme to solve propagating fronts in reaction‐diffusion equations

The Differential Quadrature Solution of Reaction-Diffusion Equation Using Explicit and Implicit Numerical Schemes

An Efficient Method to Solve Thermal Wave Equation

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