Bernstein Collocation Method for Solving Nonlinear Fredholm-Volterra Integrodifferential Equations in the Most General Form

Akyüz-Daşcıoğlu, Ayşegül; Acar, Neşe İşler; Güler, Coşkun

doi:10.1155/2014/134272

Cited by 10 publications

(4 citation statements)

References 23 publications

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“…For Fredholm-Volterra IDEs, various methods were utilized. [7]employed the projection method based on a Bernstein collocation approach; [8] used the Bernstein collocation method; [9] applied a fixed-point iterative algorithm; and [10] employed a collocation method based on Bernstein polynomials. In [11], a new numerical method was developed specifically for solving systems of Volterra 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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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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“…For Fredholm-Volterra IDEs, various methods were utilized. [10] employed the projection method based on a Bernstein collocation approach; [11] used the Bernstein collocation method; [12] applied a fixed-point iterative algorithm; [13] utilized the Chebyshev polynomial approach; and [14] employed a collocation method based on Bernstein polynomials. In [15], a new numerical method was developed specifically for solving systems of Volterra IDEs.…”

Section: Introductionmentioning

confidence: 99%

Legendre Computational Algorithm for Linear Integro-Differential Equations

Oyedepo,

Ayoade,

Ajileye

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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“…Some systematic studies of this property have been given in [1, 5-7, 11, 13-15, 18]. This method is also a powerful tool to obtain the approximate solution of nonlinear problems included such as differential equations [1,3,5,9,14,17], functional differential equations [2,7], integral equations [13,15] and integro-differential equations [4,18].…”

Section: Introductionmentioning

confidence: 99%