Second kind Chebyshev collocation technique for Volterra-Fredholm fractional  order integro-differential equations

Oyedepo, Taiye; Ayoade, Abayomi Ayotunde; Otaide, I.K.; Ayinde, A. M.

doi:10.21580/jnsmr.2022.8.2.13021

Cited by 3 publications

(3 citation statements)

References 9 publications

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“…The use of third-kind Chebyshev polynomials for solving IDEs was examined in [13] and [14]. In [15] and [16], a Computational algorithm is used to find the solution of fractional Fredholm IDEs and Volterra-Fredholm IDEs. In [17], the homotopy perturbation approach is employed for Fractional Volterra and Fredholm IDEs.…”

Section: Introductionmentioning

confidence: 99%

“…In [15] and [16], a Computational algorithm is used to find the solution of fractional Fredholm IDEs and Volterra-Fredholm IDEs. In [17], the homotopy perturbation approach is employed for Fractional Volterra and Fredholm IDEs. Other methods mentioned in this study include the quadrature-difference method [18], and Adomian's decomposition approach [19], which were used to solve Fredholm IDEs.…”

Section: Introductionmentioning

confidence: 99%

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Vieta-Lucas Polynomial Computational Tecnique for Volterra Integro-Differential Equations

Oyedepo,

Ayinde,

Didigwu

2024

Electronic Journal of Mathematical Analysis and Applications

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In this study, we introduce a computational technique for tackling Volterra Integro-Differential Equations (VIDEs) using shifted Vieta-Lucas polynomials as the foundational basis functions. The approach involves adopting an approximative solution strategy through the utilization of Vieta-Lucas polynomials. These polynomials are then integrated into the pertinent VIDEs. Subsequently, the resulting equation is subjected to collocation at evenly spaced intervals, generating a system of linear algebraic equations with unspecified Vieta-Lucas coefficients. To solve this system, we employ a matrix inversion method to deduce the unknown constants. Once these constants are determined, they are incorporated into the earlier assumed approximate solution, thus yielding the sought-after approximated solution. To validate the accuracy and efficiency of this technique, we conducted numerical experiments. The obtained results underscore the outstanding performance of our method in comparison to outcomes found in existing literature. The precision and effectiveness of the approach are further illustrated through the utilization of tables.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Vieta-Lucas Polynomial Computational Tecnique for Volterra Integro-Differential Equations

Oyedepo,

Ayinde,

Didigwu

2024

Electronic Journal of Mathematical Analysis and Applications

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“…The use of third-kind Chebyshev polynomials for solving IDEs was examined in [17] and [18]. In [19], Chebyshev Computational Approach is used to find the numerical solution Volterra-Fredholm integrodifferential equations. Other methods mentioned in this study include the Hermite collocation method [20], the extended minimal residual method [21], the quadraturedifference method [22], and Adomian's decomposition approach [23], which were used to solve Fredholm IDEs.…”

Section: Introductionmentioning

confidence: 99%

Legendre Computational Algorithm for Linear Integro-Differential Equations

OYEDEPO,

AYOADE,

AJİLEYE

et al. 2023

Cumhuriyet Science Journal

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This work presents a collocation computational algorithm for solving linear Integro-Differential Equations (IDEs) of the Fredholm and Volterra types. The proposed method utilizes shifted Legendre polynomials and breaks down the problem into a series of linear algebraic equations. The matrix inversion technique is then employed to solve these equations. To validate the effectiveness of the suggested approach, the authors examined three numerical examples. The results obtained from the proposed method were compared with those reported in the existing literature. The findings demonstrate that the proposed algorithm is not only accurate but also efficient in solving linear IDEs. In order to present the results, the study employs tables and figures. These graphical representations aid in displaying the numerical outcomes obtained from the algorithm. All calculations were performed using Maple 18 software.

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Simulation of Two-Step Block Approach for Solving Oscillatory Differential Equations

John,

Ayinde,

Oyedepo

et al. 2024

Cumhuriyet Science Journal

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This study demonstrates the derivation of a two-step block scheme simulation through a linear block approach. The scheme's fundamental properties were thoroughly analyzed and found to fulfill all necessary conditions. The research focused on examining specific classes of oscillatory differential equations and comparing them to established methods. The findings indicate that the newly proposed methods exhibit superior accuracy and faster convergence compared to the existing methods investigated in this research. Consequently, the results highlight the improved precision and quicker convergence achieved with the new method. All computations were executed using Maple 18 software

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Second kind Chebyshev collocation technique for Volterra-Fredholm fractional order integro-differential equations

Cited by 3 publications

References 9 publications

Vieta-Lucas Polynomial Computational Tecnique for Volterra Integro-Differential Equations

Vieta-Lucas Polynomial Computational Tecnique for Volterra Integro-Differential Equations

Legendre Computational Algorithm for Linear Integro-Differential Equations

Simulation of Two-Step Block Approach for Solving Oscillatory Differential Equations

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