A meshless collocation method based on Pascal polynomial approximation and implicit closest point method for solving reaction–diffusion systems on surfaces

Zamani-Gharaghoshi, Hasan; Dehghan, Mehdi; Abbaszadeh, Mostafa

doi:10.1007/s00366-023-01794-y

Cited by 4 publications

(2 citation statements)

References 42 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%

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%

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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“…In the last two decades, many fractional differential models have been studied, and these models [1]- [8] have been widely applied in many fields of science and technology, and a lot of research results have been obtained. Among them, Meerschaert and Tadjeran [4] proposed the shifted Grünwald difference operator, which combined with the Crank-Nicolson method to derive the numerical scheme of the advection-dispersion equation.…”

Section: Introductionmentioning

confidence: 99%

Crank-Nicolson Quasi-Compact Scheme for the Nonlinear Two-Sided Spatial Fractional Advection-Diffusion Equations

Gao,

Qiu,

Wang

et al. 2024

JAMP

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The higher-order numerical scheme of nonlinear advection-diffusion equations is studied in this article, where the space fractional derivatives are evaluated by using weighted and shifted Grünwald difference operators and combining the compact technique, in the time direction is discretized by the Crank-Nicolson method. Through the energy method, the stability and convergence of the numerical scheme in the sense of L 2 -norm are proved, and the convergence order is ( ). Some examples are given to show that our numerical scheme is effective.

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Investigation of phase-field models of tumor growth based on a reduced-order meshless Galerkin method

Abbaszadeh,

Dehghan,

Xiao

2023

Engineering with Computers

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A meshless collocation method based on Pascal polynomial approximation and implicit closest point method for solving reaction–diffusion systems on surfaces

Cited by 4 publications

References 42 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

Crank-Nicolson Quasi-Compact Scheme for the Nonlinear Two-Sided Spatial Fractional Advection-Diffusion Equations

Investigation of phase-field models of tumor growth based on a reduced-order meshless Galerkin method

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