Chebyshev collocation method for fractional Newell-Whitehead-Segel equation

Gebril, E.; El-Azab, M.S.; Sameeh, M.

doi:10.1016/j.aej.2023.12.025

Cited by 4 publications

(3 citation statements)

References 36 publications

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“…A wavelet-based approximation technique was presented for the numerical solutions of the Allen-Cahn and Newell-Whitehead equations [13]. For the equation, an effective haar wavelet approach was created [14], the Chebyshev collocation method [15], the Sine cosine wavelet method [16], the Sumudu decomposition method [17], Stochastic forward Euler-Stochastic nonstandard finite difference scheme [3,[18][19][20], local discontinuous Galerkin method [21], etc.…”

Section: Introductionmentioning

confidence: 99%

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A numerical investigation of a well-known nonlinear Newell-Whitehead-Segel equation using the rank polynomial of the star graph

Kumbinarasaiah,

Nirmala

2024

Phys. Scr.

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Mathematical models of pattern formation are indispensable tools in various fields, from developmental biology to ecology, providing insights into complex phenomena and contributing to our understanding of the natural world. These patterns have been extensively studied using reaction-diffusion and NewellWhiteheadSegel models. This article intended to find an approximate numerical solution to the NewellWhiteheadSegel equation. The appearance of stripe patterns in two-dimensional systems is explained in nonlinear systems using the NewellWhiteheadSegel equation. Based on the function basis of rank polynomials of star graphs and the well-posed operational matrices, the rank polynomial collocation method is constructed. The alleged rank polynomial collocation method created a system of nonlinear algebraic equations from the nonlinear NewellWhiteheadSegel equation. The nonlinear NewellWhiteheadSegel equation solution is approximated by solving the resulting system via Newton's Raphson method. Numerical instances are provided to illustrate the validity and effectiveness of the technique. Verification of accuracy is accomplished by calculating error norms. The obtained numerical results show a reasonable degree of consistency with the findings reported in the current literature. The scheme's primary benefit is the algorithm's ease of implementation.

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Section: Introductionmentioning

confidence: 99%

“…´-9.54 10 15 ´-0 varied fixed spatial and temporal points are presented in linear graphs in figures 5 and 6. The surface plots of RCM and the Exact solution's findings at various matrix sizes are presented in figures 7 and 8.…”

mentioning

confidence: 99%

A numerical investigation of a well-known nonlinear Newell-Whitehead-Segel equation using the rank polynomial of the star graph

Kumbinarasaiah,

Nirmala

2024

Phys. Scr.

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“…However, the modern development of fractional calculus gained momentum in the 19th century with the works of Liouville, Riemann, and others. There are various definitions of fractional derivatives and integrals, such as Riemann-Liouville, Grünwald-Letnikov, Caputo, conformable fractional derivative, and others, each with its own properties and applications [1][2][3]. Fractional calculus has found applications in numerous fields, including physics, engineering, signal processing, control theory, signal transmission, chemical kinematics, finance, biology, viscoelastic materials and complex fluids, anomalous diffusion phenomena, electromagnetic, nano-technology, flat wave propagation, caustic wave in crystals, digital communication, optical fibers, and more.…”

Section: Introductionmentioning

confidence: 99%

Abundant Closed-Form Soliton Solutions to the Fractional Stochastic Kraenkel–Manna–Merle System with Bifurcation, Chaotic, Sensitivity, and Modulation Instability Analysis

Borhan,

Miah,

Alsharif

et al. 2024

Fractal Fract

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An essential mathematical structure that demonstrates the nonlinear short-wave movement across the ferromagnetic materials having zero conductivity in an exterior region is known as the fractional stochastic Kraenkel–Manna–Merle system. In this article, we extract abundant wave structure closed-form soliton solutions to the fractional stochastic Kraenkel–Manna–Merle system with some important analyses, such as bifurcation analysis, chaotic behaviors, sensitivity, and modulation instability. This fractional system renders a substantial impact on signal transmission, information systems, control theory, condensed matter physics, dynamics of chemical reactions, optical fiber communication, electromagnetism, image analysis, species coexistence, speech recognition, financial market behavior, etc. The Sardar sub-equation approach was implemented to generate several genuine innovative closed-form soliton solutions. Additionally, phase portraiture of bifurcation analysis, chaotic behaviors, sensitivity, and modulation instability were employed to monitor the qualitative characteristics of the dynamical system. A certain number of the accumulated outcomes were graphed, including singular shape, kink-shaped, soliton-shaped, and dark kink-shaped soliton in terms of 3D and contour plots to better understand the physical mechanisms of fractional system. The results show that the proposed methodology with analysis in comparison with the other methods is very structured, simple, and extremely successful in analyzing the behavior of nonlinear evolution equations in the field of fractional PDEs. Assessments from this study can be utilized to provide theoretical advice for improving the fidelity and efficiency of soliton dissemination.

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New Optical Soliton Structures, Bifurcation Properties, Chaotic Phenomena, and Sensitivity Analysis of Two Nonlinear Partial Differential Equations

Borhan,

Mamun Miah,

Duraihem

et al. 2024

Int J Theor Phys

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Chebyshev collocation method for fractional Newell-Whitehead-Segel equation

Cited by 4 publications

References 36 publications

A numerical investigation of a well-known nonlinear Newell-Whitehead-Segel equation using the rank polynomial of the star graph

A numerical investigation of a well-known nonlinear Newell-Whitehead-Segel equation using the rank polynomial of the star graph

Abundant Closed-Form Soliton Solutions to the Fractional Stochastic Kraenkel–Manna–Merle System with Bifurcation, Chaotic, Sensitivity, and Modulation Instability Analysis

New Optical Soliton Structures, Bifurcation Properties, Chaotic Phenomena, and Sensitivity Analysis of Two Nonlinear Partial Differential Equations

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