Solution of Volterra-Fredholm Integro-Differential Equations Using the Chebyshev Computational Approach

Oyedepo, Taiye; Oluwayemi, Matthew O.; Ayoade, Abayomi Ayotunde; Pandurangan, Rajiniganth

doi:10.1109/seb-sdg57117.2023.10124647

Cited by 4 publications

(1 citation statement)

References 19 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%

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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