Iranian Journal of Optimization, 11(2), 149-159, December 2019 149 Shifted Chebyshev Approach for the Solution of Delay Fredholm and Volterra Integro-Differential Equations via Perturbed Galerkin Method 1 Department of Statistics and Mathematical Sciences, Kwara State University, Malete, Nigeria 2 Department of Mathematical Sciences, University of Guilan, Rasht, Iran 3 Department of Mathematics, University of Ilorin, Ilorin Nigeria Abstract The main idea proposed in this paper is the perturbed shifted Chebyshev Galerkin method for the solutions of delay Fredholm and Volterra integrodifferential equations. The application of the pro- posed method is also extended to the solutions of integro-differential difference equations. The method is validated using some selected problems from the literature. In all the problems that are considered, the new proposed approach performs better than many other meth- ods. Kazeem Issa 1* , Jafar Biazar 2 and Babatunde Morufu Yisa 3 Received: 10 January 2019 Accepted: 08 March 2019 Keywords: Delay Fredholm Delay Volterra integro-differen- tial equations Perturbed Galerkin method Shifted Chebyshev polynomials Perturbation term * Correspondence E_mail: issa.kazeem@kwasu.edu.ng Iranian Journal of Optimization Volume 11, Issue 2, 2019, 149-159 Research Paper Islamic Azad University Rasht Branch ISSN: 2588-5723 E-ISSN:2008-5427 Online version is available on: www.ijo.iaurasht.ac.ir