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All Journal Jambura Journal of Mathematics Jurnal Diferensial
ADEBISI, Ajimot Folasade
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Computer Science & IT Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Mathematics Public Health

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Numerical Solutions for Linear Integro-Differential Equations Using Shifted Legendre Basis Functions Babalola, Olutola Olayemi; ADEBISI, Ajimot Folasade
JURNAL DIFERENSIAL Vol 7 No 1 (2025): April 2025
Publisher : Program Studi Matematika, Universitas Nusa Cendana

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35508/jd.v7i1.18137

Abstract

This research explore the use of Shifted Legendre Basis functions for the numerical solution of a specific class of integro-differential equations. These equations are known for their analytical complexity,making it challenging to derive exact solutions. To address this, we employ an approximate methodusing Legendre polynomials as basis functions, which provides an efficient approach to finding solutions for these complex problems. The proposed method is computationally efficient, requiringminimal computational resources and storage. The results obtained demonstrate strong agreementwith existing solutions found in the literature, validating the accuracy and effectiveness of the approach. This study highlights the potential of Shifted Legendre Basis functions in solving challenging integro-differential equations, offering a reliable alternative to more computationally intensivemethods.
Application of the Laguerre Perturbed Galerkin Analysis Method for Solving Higher-Order Integro-Differential Equations Adebisi, Ajimot Folasade; Ojurongbe, Taiwo Adetola; Okunola, Kazeem Adekunle
Jambura Journal of Mathematics Vol 8, No 1: February 2026
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjom.v8i1.34001

Abstract

This study presents the development and implementation of a novel numerical method, the Laguerre Perturbed Galerkin (LPG) method, for solving higher-order integro-differential equations. The method leverages the advantages of Laguerre polynomials as basis functions while incorporating Chebyshev polynomials as perturbation terms to enhance both accuracy and efficiency. In the LPG method, the solution is approximated using Laguerre polynomials of degree N, with the residual error minimized via the Galerkin approach. Chebyshev polynomials are introduced as perturbation terms to further refine the solution. The residual is systematically reduced to a system of (N + 1) equations, which is then solved to determine the unknown coefficients of the approximating Laguerre polynomials. Comparative analyses demonstrate that the LPG method achieves superior accuracy and faster convergence rates compared to existing techniques, particularly for higher-order integro-differential equations. The findings contribute to the advancement of numerical methods in this domain, providing a powerful computational tool for scientists and engineers.
Perturbed Akbari-Ganji Method for the Solution of Singular Multi-Order Fractional Differential Equations Adebisi, Ajimot Folasade; Oseni, Wasiu Adewale
JURNAL DIFERENSIAL Vol 8 No 1 (2026): April 2026
Publisher : Program Studi Matematika, Universitas Nusa Cendana

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35508/jd.v8i1.20714

Abstract

Differential equations, which involve derivatives, are fundamental in describing various physical and engineering phenomena. Newton’s second law of motion provides a basic example, which illustrates how force, mass, and acceleration relate through differential equations. These equations are widely used in science and engineering to model real-world systems. Fractional differential equations extend this concept by incorporating non-integer derivatives, allowing for a more generalized approach to complex problems. Multi-order fractional equations involve multiple fractional derivatives, while singular fractional equations contain terms that become undefined at specific points. We aim to explore the significance of fractional and singular fractional differential equations in mathematical modeling, highlighting their applications in capturing intricate behaviors across different fields and our results emphasize the broader applicability of these equations in solving advanced problems in physics, engineering, and applied sciences.
Co-Authors Babalola, Olutola Olayemi Ojurongbe, Taiwo Adetola Okunola, Kazeem Adekunle Oseni, Wasiu Adewale