Computational Scheme for the Time-Fractional Reaction–Diffusion Brusselator Model

Alquran, Marwan; Jaradat, Imad; Ali, Mohammed; Aljazar, Ahlam Abu

doi:10.1007/s40819-020-00897-0

Cited by 2 publications

(3 citation statements)

References 44 publications

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“…In this section we present the error estimates and convergence of the proposed method. The proofs follow the same techniques and results as in (Hussain, 2022;Alquran et al, 2020).…”

Section: Convergence Analysismentioning

confidence: 98%

“…As the crux of RPSM is differentiation of an infinite (multiple) power series (since differentiation is relatively an easier task than integration) along with the advantages of no linearization/transformation, no discretization/round-off errors, and direct application to the given problem by choosing approximation value/function. These features make RPSM as the method of choice for a wider class of ODE and PDE problems of mathematical and physical sciences (Dubey et al, 2019;Kumar et al, 2016aKumar et al, , 2017Kumar et al, , 2016bAlquran et al, 2020;Haq and Hussain, 2018).…”

Section: Introductionmentioning

confidence: 99%

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An efficient iterative scheme for the analytical-numerical solution of multi-dimensional nonlinear Burgers' equations

Hussain

Farooq

Ghafoor

2022

Preprint

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This article proposes a simple yet efficient/powerful iterative scheme to obtain approximate solutions to a class of nonlinear parabolic partial differential equations. The approximation method is based on the residual error function and the multiple power series expansion. Error estimates are derived and convergence of the proposed method is established. Several numerical examples are then considered to validate the theoretical results and highlight the computational ease of the developed residual power series method on multi-dimensional nonlinear Burgers’ equations. It is observed that the proposed approximation method captures shock wave propagation and steep gradient formation very well, and delivers more accurate results than the contemporary methods in higher dimensions.

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“…In this section we present the error estimates and convergence of the proposed method. The proofs follow the same techniques and results as in (Hussain, 2022;Alquran et al, 2020).…”

Section: Convergence Analysismentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

An efficient iterative scheme for the analytical-numerical solution of multi-dimensional nonlinear Burgers' equations

Hussain

Farooq

Ghafoor

2022

Preprint

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“…In short, delay partial differential equations (DPDEs), and Time-Fractional Delay Partial Differential Equations (TFDPDEs) not only model physical problems that depend on the current state of the system, but also on past history. Several such examples can be seen in recent literature as [1][2][3][4][5][6][7]14]. They solved fractional delay differential equations like Newell-Whitehead-Segel system, fractional delay type wave equation, fractional Boussinesq-Burgers equation, fractional twomode Korteweg-De Vries equation, fractional reaction-Diffusion Brusselator model, and Duffing equation by many interesting techniques and obtained several fascinating results.…”

Section: Introductionmentioning

confidence: 99%

Numerical Solution of Time Fractional Delay Partial Differential Equations by Perturbation Iteration Algorithm

2021

Punjab Univ. j. math.

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The aim of this research was to relate two physical effects for partial differential equations on the time-coordinate, notably the multipledelay times and fractional-derivative. Time Fractional Delay Partial Differential Equations (TFDPDEs) usually interpret some complex physical phenomenon. This study works to solve TFDPDE with shrinking in x and proportional delays in t numerically by utilizing the fractional derivative of Caputo sense in the numerical method known as Perturbation Iteration Algorithm (PIA). A few famous numerical examples have been solved using PIA and their comparison with an exact solutions is illustrated for ® = 1. Also, different values of ® have been depicted in graphical form to show their fractional behavior. The delay term k is also discussed extensively in this TFDPDE study. Numerical results show that this technique is reliable, convenient, and attractive for computational use in modern times.

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Computational Scheme for the Time-Fractional Reaction–Diffusion Brusselator Model

Cited by 2 publications

References 44 publications

An efficient iterative scheme for the analytical-numerical solution of multi-dimensional nonlinear Burgers' equations

An efficient iterative scheme for the analytical-numerical solution of multi-dimensional nonlinear Burgers' equations

Numerical Solution of Time Fractional Delay Partial Differential Equations by Perturbation Iteration Algorithm

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