Using adomian’s decomposition and multiquadric quasi-interpolation methods for solving Newell–Whitehead equation

Ezzati, Reza; Shakibi, K.

doi:10.1016/j.procs.2010.12.171

Cited by 26 publications

(15 citation statements)

References 12 publications

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“…The second equation is known as the Newell-Whitehead-Segel equation [30] and describes the envelope of a modulated roll-solution in systems with too large extended or unbounded equations [31]. It is given by…”

Section: B Newell-whitehead-segel Equationmentioning

confidence: 79%

“…The second equation is known as the Newell–Whitehead–Segel equation and describes the envelope of a modulated roll‐solution in systems with too large extended or unbounded equations . It is given by

\frac{\partial U}{\partial t} = \frac{\partial^{2} U}{\partial x^{2}} + U (1 - U^{α}) .

An analytical solution to this equation is

U (x, t) = {true{\frac{1}{2} \tan h true{- \frac{α}{2 \sqrt{2 α + 4}} true(x - \frac{α + 4}{\sqrt{2 α + 4}} t true) true} + \frac{1}{2} true}}^{2 / α},

which was obtained by Wang , Wazwaz and Gorguis , Ağirseven and Öziş , and Aminikhah et.…”

Section: Results Of the Numerical Simulationmentioning

confidence: 99%

See 1 more Smart Citation

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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Section: B Newell-whitehead-segel Equationmentioning

confidence: 79%

\frac{\partial U}{\partial t} = \frac{\partial^{2} U}{\partial x^{2}} + U (1 - U^{α}) .

An analytical solution to this equation is

U (x, t) = {true{\frac{1}{2} \tan h true{- \frac{α}{2 \sqrt{2 α + 4}} true(x - \frac{α + 4}{\sqrt{2 α + 4}} t true) true} + \frac{1}{2} true}}^{2 / α},

which was obtained by Wang , Wazwaz and Gorguis , Ağirseven and Öziş , and Aminikhah et.…”

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

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“…Kheiri et al [11] developed Homotopy analysis and Homotopy Pade methods for solving the modified Burgers-Korteweg-de Vries and the Newell-Whitehead equations. Ezzati and Shakibi [6] used the Adomian's Decomposition and multi-quadric qausi-interpolation techniques to obtain the solution of NWS equation. Macias-Diaz and Ramirez [12] computed numerical results for gNWS equation using finite difference algorithm.…”

Section: Introductionmentioning

confidence: 99%

Exponential B-spline collocation method for solving the generalized Newell-Whitehead-Segel equation

Wasim¹,

Abbas²,

Iqbal³

et al. 2020

J. Math. Computer Sci.

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In this work, we present a collocation method based on exponential basis spline functions for solving generalized Newell-Whitehead-Segel equation. The time derivative is discretized by finite difference scheme and the exponential basis spline functions are employed to interpolate spatial derivatives. The convergence and stability of the proposed algorithm are established. Numerical results demonstrate the accuracy of the proposed method.

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“…Also, the Newell‐Whitehead equation was solved by several methods, too. The equation was solved using Adomian's decomposition and multiquadric quasi‐interpolation methods . Approximation solution was obtained for the equation by homotopy analysis and homotopy Padé methods .…”

Section: Introductionmentioning

confidence: 99%

Analytical and numerical solutions of mathematical biology models: The Newell‐Whitehead‐Segel and Allen‐Cahn equations

İnan

Osman

et al. 2019

Math Methods in App Sciences

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In this paper, we combine the unified and the explicit exponential finite difference methods to obtain both analytical and numerical solutions for the Newell‐Whitehead‐Segel–type equations which are very important in mathematical biology. The unified method is utilized to obtain various solitary wave solutions for these equations. Numerical solutions of the specific case studies are investigated by using the explicit exponential finite difference method ensures the accuracy and reliability of the proposed scheme. After obtaining the approximate solutions, convergence analysis and error estimation (the error norms and absolute errors) are presented by comparing these results with the analytical obtained solutions and other methods in the literature through tables and graphs. The obtained analytical and numerical results are in good agreement.

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Using adomian’s decomposition and multiquadric quasi-interpolation methods for solving Newell–Whitehead equation

Cited by 26 publications

References 12 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

Exponential B-spline collocation method for solving the generalized Newell-Whitehead-Segel equation

Analytical and numerical solutions of mathematical biology models: The Newell‐Whitehead‐Segel and Allen‐Cahn equations

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