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Jambura Journal of Mathematics
Published by Universitas Negeri Gorontalo
ISSN : 26545616     EISSN : 26561344     DOI : https://doi.org/10.34312/jjom
Core Subject : Education,
Mathematics
Jambura Journal of Mathematics (JJoM) is a peer-reviewed journal published by Department of Mathematics, State University of Gorontalo. This journal is available in print and online and highly respects the publication ethic and avoids any type of plagiarism. JJoM is intended as a communication forum for mathematicians and other scientists from many practitioners who use mathematics in research. The scope of the articles published in this journal deal with a broad range of topics, including: Mathematics; Applied Mathematics; Statistics; Applied Statistics.
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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 Articles in press
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

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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. This method leverages the advantages of Laguerre polynomials as basis functions while incorporating Chebyshev polynomials as perturbation terms to enhance accuracy and efficiency. In the LPG method, the solution is approximated using Laguerre polynomials of degree (N), with the residual error minimized via a Galerkin approach. The Chebyshev polynomials serve as perturbation terms to refine the accuracy of the solution. The residual is systematically reduced to an (n+1) system of equations, which is then solved to determine the unknown coefficients of the approximating Laguerre polynomials. Comparative analyses demonstrate that the method achieves superior accuracy and convergence rates compared to existing techniques, particularly for higher-order integro-differential equations. The findings contribute significantly to the advancement of numerical methods in this domain, providing a powerful computational tool for scientists and engineers.

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