Solving Fractional Generalized Fisher–Kolmogorov–Petrovsky–Piskunov’s Equation Using Compact-Finite Different Methods Together with Spectral Collocation Algorithms

Youssef, Maged Z.; Khader, M. M.; Al-Dayel, İbrahim; Ahmed, W. Eltayeb

doi:10.1155/2022/1901131

Cited by 8 publications

(4 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The inner product of V ) and other properties are given in (Issa et al, 2024); (Agarwal and El-Sayed, 2020); (Youssef et. al., 2022).…”

Section: Preliminariesmentioning

confidence: 99%

Numerical Solution of Generalized Delay Integro-Differential Equations via Galerkin-Vieta-Lucas Polynomials

Issa,

Sulaiman,

Olabamidele

et al. 2024

IJDM

View full text Add to dashboard Cite

In this article, the Galerkin-Vieta-Lucas scheme is presented to find an approximate solution to the generalised delay integro-differential equation using the Vieta-Lucas polynomial as an approximation. The Galerkin approach transforms the delay integro-differential equation into a set of n × (n + m) algebraic equations, which, together with the attached conditions, give (n + m) × (n + m) equations. The effectiveness and accuracy of the proposed technique were tested on some existing examples in the literature, and obviously, the results obtained justify the accuracy of the proposed scheme.

show abstract

“…The inner product of V ) and other properties are given in (Issa et al, 2024); (Agarwal and El-Sayed, 2020); (Youssef et. al., 2022).…”

Section: Preliminariesmentioning

confidence: 99%

Numerical Solution of Generalized Delay Integro-Differential Equations via Galerkin-Vieta-Lucas Polynomials

Issa,

Sulaiman,

Olabamidele

et al. 2024

IJDM

View full text Add to dashboard Cite

show abstract

“…Here, we used an approximate formula of D (n) ψ m (η) of the approximated function ψ m (η) defned in form (18), where the authors in [25] derived this formula in the following form:…”

Section: Approximate the Solutionmentioning

confidence: 99%

“…For more details about these polynomials and the convergence analysis of approximations ( 18) and (19), see [25].…”

Section: Approximate the Solutionmentioning

confidence: 99%

Vieta-Lucas Collocation Technique for Examination of the Flow of Casson Fluid over a Slippery Stretching Sheet Which Is Impacted by Thermal Slip, Ohmic Dissipation, and Variable Thermal Conductivity

Eid

Khader

Megahed

2023

Journal of Mathematics

Self Cite

View full text Add to dashboard Cite

This work aimed to present the influence of the magnetic field and Ohmic dissipation on the non-Newtonian Casson fluid on a vertical stretched sheet to numerically solve the problem. Here, the variable thermal conductivity is taken as a linear function of temperature. Electric fields, thermal slip, and viscous dissipation effects are taken into consideration. A collection of physical conditions on the sheet’s enclosing wall and the momentum and heat transport processes are expressed as partial differential equations (PDEs). Some of the similarity transformations are used to convert the collection of PDE into a system of ordinary differential equations. This system is numerically treated by implementing the Vieta-Lucas spectral collocation method. Some observations are made for the investigation of method convergence. The effect of some different parameters on the velocity and temperature profiles is graphically represented. Additionally, this area of study has significant practical applications in a variety of industries, including paper production, thermal power generation, nuclear reactors, cooling of metallic sheets, glass fiber, and lubrication.

show abstract

“…The capacity of the FDM to solve problems that occur in calculations with other numerical methods, such as the finite element approach [12], has been noted by numerous scholars [13] [14]. This technique has been utilized to solve various problems [15] [16] [17].…”

Section: Introductionmentioning

confidence: 99%

Numerical Study by Imposing the Finite Difference Method for Unsteady Casson Fluid Flow with Heat Flux

Tedjani

2023

JAMP

View full text Add to dashboard Cite

This article presents an investigation into the flow and heat transfer characteristics of an impermeable stretching sheet subjected to Magnetohydrodynamic Casson fluid. The study considers the influence of slip velocity, thermal radiation conditions, and heat flux. The investigation is conducted employing a robust numerical method that accounts for the impact of thermal radiation. This category of fluid is apt for characterizing the movement of blood within an industrial artery, where the flow can be regulated by a material designed to manage it. The resolution of the ensuing system of ordinary differential equations (ODEs), representing the described problem, is accomplished through the application of the finite difference method. The examination of flow and heat transfer characteristics, including aspects such as unsteadiness, radiation parameter, slip velocity, Casson parameter, and Prandtl number, is explored and visually presented through tables and graphs to illustrate their impact. On the stretching sheet, calculations, and descriptions of the local skin-friction coefficient and the local Nusselt number are conducted. In conclusion, the findings indicate that the proposed method serves as a straightforward and efficient tool for exploring the solutions of fluid models of this kind.

show abstract

Solving Fractional Generalized Fisher–Kolmogorov–Petrovsky–Piskunov’s Equation Using Compact-Finite Different Methods Together with Spectral Collocation Algorithms

Cited by 8 publications

References 28 publications

Numerical Solution of Generalized Delay Integro-Differential Equations via Galerkin-Vieta-Lucas Polynomials

Numerical Solution of Generalized Delay Integro-Differential Equations via Galerkin-Vieta-Lucas Polynomials

Vieta-Lucas Collocation Technique for Examination of the Flow of Casson Fluid over a Slippery Stretching Sheet Which Is Impacted by Thermal Slip, Ohmic Dissipation, and Variable Thermal Conductivity

Numerical Study by Imposing the Finite Difference Method for Unsteady Casson Fluid Flow with Heat Flux

Contact Info

Product

Resources

About