Numerical algorithm for a generalized form of Schnakenberg reaction-diffusion model with gene expression time delay

Omran, A.K.; Zaky, Mahmoud A.; Hendy, Ahmed S.; Пименов, В. Г.

doi:10.1016/j.apnum.2022.11.024

Cited by 4 publications

(2 citation statements)

References 44 publications

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“…Then, the coefficients will be chosen such the absolute error is minimized as well as possible. Whilst, the numerical solution will be implemented almost to satisfy differential equations in spectral collocation technique [24][25][26][27][28][29]. On the other hand, the residuals may be permitted to be zero at selection points.…”

Section: Introductionmentioning

confidence: 99%

Spectral technique with convergence analysis for solving one and two-dimensional mixed Volterra-Fredholm integral equation

Amin

Abdelkawy

et al. 2023

PLoS ONE

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A numerical approach based on shifted Jacobi-Gauss collocation method for solving mixed Volterra-Fredholm integral equations is introduced. The novel technique with shifted Jacobi-Gauss nodes is applied to reduce the mixed Volterra-Fredholm integral equations to a system of algebraic equations that has an easy solved. The present algorithm is extended to solve the one and two-dimensional mixed Volterra-Fredholm integral equations. Convergence analysis for the present method is discussed and confirmed the exponential convergence of the spectral algorithm. Various numerical examples are approached to demonstrate the powerful and accuracy of the technique.

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Section: Introductionmentioning

confidence: 99%

Spectral technique with convergence analysis for solving one and two-dimensional mixed Volterra-Fredholm integral equation

Amin

Abdelkawy

et al. 2023

PLoS ONE

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“…Fan and Jiang [10] consider an unstructured mesh finite element method for the two-dimensional time-space fractional Schrödinger equation. High-order numerical schemes for time-space fractional differential equations with variable-order fractional derivatives or delay can be found in the work of Zaky et al [11][12][13][14][15]. Furthermore, the L1 Galerkin methods are proposed for the case with nonsmooth solution [16,17].…”

Section: Introductionmentioning

confidence: 99%

L1/LDG algorithm for time‐Caputo space‐Riesz fractional convection equation in two dimensions

Cai,

2023

Math Methods in App Sciences

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This paper proposes an L1/LDG algorithm for a time–space fractional convection equation on a bounded rectangular domain . Here, the temporal partial derivative is in the sense of Caputo with order , and the spatial partial derivatives are of Riesz type with orders in ‐ and ‐directions, respectively. L1 approximation is utilized to evaluate the temporal Caputo derivative, while the local discontinuous Galerkin (LDG) method is adopted to deal with the spatial Riesz derivative. The rigorous numerical stability analysis and error estimate are presented which are supported by illustrative numerical examples.

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Efficiently solving fractional delay differential equations of variable order via an adjusted spectral element approach

Ayazi,

Mokhtary,

Moghaddam

2024

Chaos, Solitons & Fractals

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Numerical algorithm for a generalized form of Schnakenberg reaction-diffusion model with gene expression time delay

Cited by 4 publications

References 44 publications

Spectral technique with convergence analysis for solving one and two-dimensional mixed Volterra-Fredholm integral equation

Spectral technique with convergence analysis for solving one and two-dimensional mixed Volterra-Fredholm integral equation

L1/LDG algorithm for time‐Caputo space‐Riesz fractional convection equation in two dimensions

Efficiently solving fractional delay differential equations of variable order via an adjusted spectral element approach

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