Pell Collocation Pseudo Spectral Scheme for One-Dimensional Time-Fractional Convection Equation with Error Analysis

Mohamed, Amany S.

doi:10.1155/2022/9734604

Cited by 3 publications

(1 citation statement)

References 21 publications

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“…It is a suitable method for dealing with non-linear equations. For example: [8][9][10][11][12] using the collocation method for studying nonlinear FDEs (subject to initial/boundary conditions), studying the second-order multipoint boundary value problems, solving nonlinear FDEs subject to initial/boundary conditions, solving multi-term fractional differential equations, and solving one-dimensional time-fractional convection equation. The last technique, tau, works by decreasing the residual of the differential equation and then applying the initial and boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Spectral Collocation Algorithm for Solving Fractional Volterra-Fredholm Integro-Differential Equations via Generalized Fibonacci Polynomials

Abo-Eldahab

Mohamed

Ali

2022

Contemporary Mathematics

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In this research article, we build and implement an efficient spectral algorithm for handling linear/nonlinear mixed Volterra-Fredholm integro-differential equations. First, we expand the exact solution as a truncated series of the generalized Fibonacci polynomials, and then we discretize the equation via Simpson's quadrature formula. Finally, we collocate the resulted residual at the roots of the shifted first-kind Chebyshev polynomials. Also, the rate of convergence is studied and the truncation error estimate is reported. Some numerical examples are exhibited to prove the applicability and accuracy of the algorithm.

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Section: Introductionmentioning

confidence: 99%

Spectral Collocation Algorithm for Solving Fractional Volterra-Fredholm Integro-Differential Equations via Generalized Fibonacci Polynomials

Abo-Eldahab

Mohamed

Ali

2022

Contemporary Mathematics

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New convolved Fibonacci collocation procedure for the Fitzhugh–Nagumo non-linear equation

Abd-Elhameed,

Al-Harbi,

Atta

2024

Nonlinear Engineering

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This article is dedicated to propose a spectral solution for the non-linear Fitzhugh–Nagumo equation. The proposed solution is expressed as a double sum of basis functions that are chosen to be the convolved Fibonacci polynomials that generalize the well-known Fibonacci polynomials. In order to be able to apply the proposed collocation method, the operational matrices of derivatives of the convolved Fibonacci polynomials are introduced. The convergence and error analysis of the double expansion are carefully investigated in detail. Some new identities and inequalities regarding the convolved Fibonacci polynomials are introduced for such a study. Some numerical results, along with some comparisons, are provided. The presented results show that our proposed algorithm is efficient and accurate.

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New formulas of convolved Pell polynomials

Abd-Elhameed,

Napoli

2024

MATH

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<abstract><p>The article investigates a class of polynomials known as convolved Pell polynomials. This class generalizes the standard class of Pell polynomials. New formulas related to convolved Pell polynomials are established. These formulas may be useful in different applications, in particular in numerical analysis. New expressions are derived for the high-order derivatives of these polynomials, both in terms of their original polynomials and in terms of various well-known polynomials. As special cases, connection formulas linking the convolved Pell polynomials with some other polynomials can be deduced. The new moments formula of the convolved Pell polynomials that involves a terminating hypergeometric function of the unit argument is given. Then, some reduced specific moment formulas are deduced based on the reduction formulas of some hypergeometric functions. Some applications, including new specific definite and weighted definite integrals, are deduced based on some of the developed formulas. Finally, a matrix approach for this kind of polynomial is presented.</p></abstract>

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Pell Collocation Pseudo Spectral Scheme for One-Dimensional Time-Fractional Convection Equation with Error Analysis

Cited by 3 publications

References 21 publications

Spectral Collocation Algorithm for Solving Fractional Volterra-Fredholm Integro-Differential Equations via Generalized Fibonacci Polynomials

Spectral Collocation Algorithm for Solving Fractional Volterra-Fredholm Integro-Differential Equations via Generalized Fibonacci Polynomials

New convolved Fibonacci collocation procedure for the Fitzhugh–Nagumo non-linear equation

New formulas of convolved Pell polynomials

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