156567ec-0287-42e1-ae3a-bf122c29923920250916063911206wseas:wseasmdt@crossref.orgMDT DepositPROOF2732-99412944-916210.37394/232020https://wseas.com/journals/proof/index.php12720251272025510.37394/232020.2025.5https://wseas.com/journals/proof/2025.phpT.OyedepoDepartment of Health Information Management, Federal University of Allied Health Sciences, Enugu, 400001, NIGERIAhttps://orcid.org/0000-0001-9063-8806M. O.OluwayemiDepartment of Computer Science, Margaret Lawrence University, Galilee, Delta State, NIGERIAhttps://orcid.org/0000-0003-3170-6818RajiniganthPDepartment of Mathematics, Dhanalakshmi Srinivasan University, Samayapuram-621112, Tiruchirapalli, Tamil Nadu, INDIAhttps://orcid.org/0000-0002-3817-0588A. A.AyoadeDepartment of Mathematics, University of Lagos, Akoka, Lagos State, NIGERIAIntegro-differential equations (IDEs) seamlessly blend differential and integral operators, offering a versatile mathematical framework for modelling various physical, biological, and engineering systems. Analytical solutions to these equations are often unattainable due to their complexity, necessitating efficient numerical approaches. This study introduces the Legendre Collocation Method (LCM), leveraging shifted Legendre polynomials to approximate solutions for Volterra and Fredholm IDEs. By transforming the IDEs into a system of linear equations, the proposed method achieves high accuracy and computational efficiency. Numerical experiments on representative IDEs validate the approach, showing excellent agreement with exact solutions and outperforming existing methods in terms of absolute error. These results underscore the potential of the LCM in solving complex IDEs with broad applicability across disciplines.91620259162025667310https://wseas.com/journals/proof/2025/a20proof-007(2025).pdf10.37394/232020.2025.5.10https://wseas.com/journals/proof/2025/a20proof-007(2025).pdfI. Podlubny, Fractional Differential Equations, Academic Press, (1999). 10.1017/cbo9780511543234H. Brunner, Collocation methods for Volterra integral and related functional equations, Cambridge University Press (2004). K. Atkinson, The Numerical Solution of Integral Equations of the Second Kind. Cambridge University Press, (1997). https://doi.org/10.1017/CBO9780511626340 P. Linz, Analytical and numerical methods for Volterra equations. SIAM. (1985). J. Hale, H. Kocak, & H. Liu, Dynamics and Bifurcations, Springer-Verlag. (2009). 10.11648/j.acm.20140301.12A. Filiz (2013). 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Numerical Implementation of a Susceptible - Infected - Recovered (SIR) Mathematical Model of Covid-19 Disease in Nigeria, WSEAS Transactions on Biology and Biomedicine, 65- 74, doi: 10.37394/23208.2024.21.7.