Eshkuvatov Z.K.Kammuji M.Yunus A.A.M.2024-05-292024-05-29201897807400000000094243X10.1063/1.50416392-s2.0-85049807503https://www.scopus.com/inward/record.uri?eid=2-s2.0-85049807503&doi=10.1063%2f1.5041639&partnerID=40&md5=36f705090fdbef168895775843728217https://oarep.usim.edu.my/handle/123456789/10380WOS:000443958400108Proceeding of the 25th National Symposium on Mathematical Sciences (SKSM25)AIP Conf. Proc. 1974, 020108-1–020108-8; https://doi.org/10.1063/1.5041639 Published by AIP Publishing. 978-0-7354-1681-9 $30.In this note, a general form of Fredholm-Volterra integro-differential equation order one is considered. The truncated Legendre series is used as bases function to approximate unknown function and Gauss-Legendre quadrature formula is applied for kernel integrals. Reduced algebraic equations are solved by using collocation method with roots of Legendre polynomials as collocation points. Three numerical examples with the comparisons are provided to show the validity and accuracy of the suggested method. Numerical results reveal that proposed method is dominated with repeated trapezoidal rule and differential transform method. � 2018 Author(s).en-US2000 MSC: 45B0545A0545L05ApproximationsCollocation methodIntegro-differential equationsLegendre polynomialsArticle197420108