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Ishola, Christie Yemisi
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Agriculture, Biological Sciences & Forestry Biochemistry, Genetics & Molecular Biology Chemistry Materials Science & Nanotechnology Physics

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Numerical computational approach for 6th order boundary value problems Adebisi, Folasade Ajimot; Ishola, Christie Yemisi; Uwaheren, Ohigweren Airenoni; Okunola, Kamilu Adedokun; Raji, Musiliu Tayo; Oseni, Wasiu
Journal of Natural Sciences and Mathematics Research Vol. 9 No. 1 (2023): June
Publisher : Faculty of Science and Technology, Universitas Islam Negeri Walisongo Semarang

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Abstract

This study introduces numerical computational methods that employ fourth-kind Chebyshev polynomials as basis functions to solve sixth-order boundary value problems. The approach transforms the BVPs into a system of linear algebraic equations, expressed as unknown Chebyshev coefficients, which are subsequently solved through matrix inversion. Numerical experiments were conducted to validate the accuracy and efficiency of the technique, demonstrating its simplicity and superiority over existing solutions. The graphical representation of the method's solution is also presented.
Legendre Collocation approach for Integro-Differential equations Oyedepo, Taiye; AYOADE, Abayomi Ayotunde; ISHOLA, Christie Yemisi; AYINDE , Addullahi Muhammed
Journal of Natural Sciences and Mathematics Research Vol. 11 No. 1 (2025): June
Publisher : Faculty of Science and Technology, Universitas Islam Negeri Walisongo Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21580/jnsmr.v11i1.25114

Abstract

This study presents the application of the Legendre Collocation Method (LCM) for solving Integro-Differential Equations (IDEs), which model a range of scientific and engineering problems.IDEs, involving both differential and integral terms, often require numerical methods for their solutions due to the complexity of obtaining exact solutions. The proposed approach transforms IDEs into systems of linear algebraic equations using shifted Legendre polynomials. By collocating the resulting equations, approximate solutions are efficiently computed. The accuracy of the method is validated through several numerical examples, including Volterra and Fredholm types of IDEs, and the results are compared with known exact solutions. The effectiveness and robustness of LCM are demonstrated through high-order approximations. The theoretical uniqueness of the method is established using relevant theorems, including the Banach Contraction Principle. Overall, the LCM provides a reliable and efficient technique for solving a wide class of IDEs with high accuracy. 
Co-Authors ADEBISI, Folasade Ajimot AYINDE , Addullahi Muhammed AYOADE, Abayomi Ayotunde Okunola, Kamilu Adedokun Oseni, Wasiu Oyedepo, Taiye Raji, Musiliu Tayo Uwaheren, Ohigweren Airenoni