An Approximate Solution to The Newell-Whitehead Equation by Adomian Decomposition Method

Manaa, Saad A.

doi:10.33899/csmj.2011.163617

Cited by 6 publications

(6 citation statements)

References 21 publications

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“…If we take a = 1, the fractional NWSE reduces to the classical NWSE (Macías-Díaz and Ruiz-Ramírez, 2011). The classical NWSE have been studied by Laplace Adomian decomposition method (Pue-on, 2013), Differential transform method (Aasaraai, 2011), Reduced Differential transform method (Saravanan and Magesh, 2013), Adomian decomposition method (Manaa, 2011), Homotopy perturbation method (HPM; Nourazar et al, 2011;Mahgoub, 2016), Cubic B-spline collocation algorithm (Zahra et al, 2014) and Variational iteration method . Some recent advances on HPM can be found in Skrzypacz et al, 2020;Anjum and He, 2020;In the past few decades, it has been observed that fractional analysis has tremendous applications in many branches of science.…”

Section: Introductionmentioning

confidence: 99%

The homotopy perturbation method for fractional differential equations: part 1 Mohand transform

Nadeem

Islam

2021

HFF

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Purpose This study aims that very lately, Mohand transform is introduced to solve the ordinary and partial differential equations (PDEs). In this paper, the authors modify this transformation and associate it with a further analytical method called homotopy perturbation method (HPM) for the fractional view of Newell–Whitehead–Segel equation (NWSE). As Mohand transform is restricted to linear obstacles only, as a consequence, HPM is used to crack the nonlinear terms arising in the illustrated problems. The fractional derivatives are taken into the Caputo sense. Design/methodology/approach The specific objective of this study is to examine the problem which performs an efficient role in the form of stripe orders of two dimensional systems. The authors achieve the multiple behaviors and properties of fractional NWSE with different positive integers. Findings The main finding of this paper is to analyze the fractional view of NWSE. The obtain results perform very good in agreement with exact solution. The authors show that this strategy is absolutely very easy and smooth and have no assumption for the constriction of this approach. Research limitations/implications This paper invokes these two main inspirations: first, Mohand transform is associated with HPM, secondly, fractional view of NWSE with different positive integers. Practical implications In this paper, the graph of approximate solution has the excellent promise with the graphs of exact solutions. Social implications This paper presents valuable technique for handling the fractional PDEs without involving any restrictions or hypothesis. Originality/value The authors discuss the fractional view of NWSE by a Mohand transform. The work of the present paper is original and advanced. Significantly, to the best of the authors’ knowledge, no such work has yet been published in the literature.

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Section: Introductionmentioning

confidence: 99%

The homotopy perturbation method for fractional differential equations: part 1 Mohand transform

Nadeem

Islam

2021

HFF

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“…Furthermore, this equation has been applied to various systems, e.g., nonlinear optics, biological systems, Rayleigh-Benard convection, and chemical reactions. In recent years, several techniques have been developed to solve the NWS equations, e.g., lattice Bolzmann scheme [14], Adomian decomposition method [15], finite difference scheme [16], differential transformation method [17], and reduced differential transformation [18].…”

Section: Introductionmentioning

confidence: 99%

Exact Solutions of Newell-Whitehead-Segel Equations Using Symmetry Transformations

Bibi

Ahmad

2021

Journal of Function Spaces

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In this article, Lie and discrete symmetry transformation groups of linear and nonlinear Newell-Whitehead-Segel (NWS) equations are obtained. By using these symmetry transformation groups, several group invariant solutions of considered NWS equations have been constructed. Furthermore, some more group invariant solutions are generated by using discrete symmetry transformation group. Graphical representations of some obtained solutions are also presented.

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“…, expresses the variations of ϑ(x, t) with spatial variable x at a specific time and the remaining terms on the right hand side, αϑ − βϑ γ , takes into account the effect of the source term. Recently, NWSE has been studied by Laplace Adomian decomposition method [31], Adomian decomposition method [24], differential transform method [1], cubic B-spline collection method [40], VIM [30] and HPM [21,28,29]. In current paper, we will study the VIM combined with HPM.…”

Section: Introductionmentioning

confidence: 99%

Solution of Newell-Whitehead-Segel equation by variational iteration method with He's polynomials

Nadeem¹,

Yao²,

Parveen³

2019

J. Math. Computer Sci.

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This article seeks to extend the variational iteration method (VIM) with He's polynomials for the approximate solution of nonlinear Newell-Whitehead-Segel equation (NWSE). Lagrange multiplier in correction functional is determined with the help of variational theory, and then homotopy perturbation method (HPM) is employed to dissolve the nonlinear terms. Thus a successful series is obtained with these iterations which are termed as He's polynomials. Result shows that this method is highly accurate and comes closer very quickly to the exact solution. We formulate three possible cases of NWSE to show the capability and ability of the present method. The valuable outcome discloses that the proposed strategy is very convenient, straightforward and can be utilized to linear and nonlinear problems.

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An Approximate Solution to The Newell-Whitehead Equation by Adomian Decomposition Method

Cited by 6 publications

References 21 publications

The homotopy perturbation method for fractional differential equations: part 1 Mohand transform

The homotopy perturbation method for fractional differential equations: part 1 Mohand transform

Exact Solutions of Newell-Whitehead-Segel Equations Using Symmetry Transformations

Solution of Newell-Whitehead-Segel equation by variational iteration method with He's polynomials

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