Global Conference on Mathematics and Applications (GCMA)

In this work, we propose a numerical collocation method for solving linear Fredholm integro-differential equations using shifted Chebyshev polynomials of the third kind. The approximate solution, its derivatives, and the integral operator are expressed in matrix form, leading to a system of algebraic equations in which the initial conditions are incorporated directly. Numerical experiments demonstrate the effectiveness and accuracy of the proposed method, with small absolute errors obtained for the considered test problems.