Legendre Computational Algorithm for Linear Integro-Differential Equations

Taiye Oyedepo; Abayomi Ayoade; Ganiyu Ajileye; Nneoma Joyce Ikechukwu

doi:10.17776/csj.1267158

EN

Legendre Computational Algorithm for Linear Integro-Differential Equations

Abstract

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.

Keywords

Legendre polynomials, Fredholm and Volterra integro-differential equations, Approximate solution

References

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Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Taiye Oyedepo ^*
0000-0001-9063-8806
Nigeria

Abayomi Ayoade
0000-0003-3470-0147
Nigeria

Ganiyu Ajileye This is me
0000-0002-4161-686X
Nigeria

Nneoma Joyce Ikechukwu
0000-0001-9049-3037
Nigeria

Publication Date

September 29, 2023

Submission Date

March 18, 2023

Acceptance Date

September 7, 2023

Published in Issue

Year 2023 Volume: 44 Number: 3

DOI

https://doi.org/10.17776/csj.1267158

IZ

https://izlik.org/JA67KP85BT

APA

Oyedepo, T., Ayoade, A., Ajileye, G., & Ikechukwu, N. J. (2023). Legendre Computational Algorithm for Linear Integro-Differential Equations. Cumhuriyet Science Journal, 44(3), 561-566. https://doi.org/10.17776/csj.1267158

AMA

1.Oyedepo T, Ayoade A, Ajileye G, Ikechukwu NJ. Legendre Computational Algorithm for Linear Integro-Differential Equations. CSJ. 2023;44(3):561-566. doi:10.17776/csj.1267158

Chicago

Oyedepo, Taiye, Abayomi Ayoade, Ganiyu Ajileye, and Nneoma Joyce Ikechukwu. 2023. “Legendre Computational Algorithm for Linear Integro-Differential Equations”. Cumhuriyet Science Journal 44 (3): 561-66. https://doi.org/10.17776/csj.1267158.

EndNote

Oyedepo T, Ayoade A, Ajileye G, Ikechukwu NJ (September 1, 2023) Legendre Computational Algorithm for Linear Integro-Differential Equations. Cumhuriyet Science Journal 44 3 561–566.

IEEE

[1]T. Oyedepo, A. Ayoade, G. Ajileye, and N. J. Ikechukwu, “Legendre Computational Algorithm for Linear Integro-Differential Equations”, CSJ, vol. 44, no. 3, pp. 561–566, Sept. 2023, doi: 10.17776/csj.1267158.

ISNAD

Oyedepo, Taiye - Ayoade, Abayomi - Ajileye, Ganiyu - Ikechukwu, Nneoma Joyce. “Legendre Computational Algorithm for Linear Integro-Differential Equations”. Cumhuriyet Science Journal 44/3 (September 1, 2023): 561-566. https://doi.org/10.17776/csj.1267158.

JAMA

1.Oyedepo T, Ayoade A, Ajileye G, Ikechukwu NJ. Legendre Computational Algorithm for Linear Integro-Differential Equations. CSJ. 2023;44:561–566.

MLA

Oyedepo, Taiye, et al. “Legendre Computational Algorithm for Linear Integro-Differential Equations”. Cumhuriyet Science Journal, vol. 44, no. 3, Sept. 2023, pp. 561-6, doi:10.17776/csj.1267158.

Vancouver

1.Taiye Oyedepo, Abayomi Ayoade, Ganiyu Ajileye, Nneoma Joyce Ikechukwu. Legendre Computational Algorithm for Linear Integro-Differential Equations. CSJ. 2023 Sep. 1;44(3):561-6. doi:10.17776/csj.1267158

Cited By

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

Cumhuriyet Science Journal

https://doi.org/10.17776/csj.1345303

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