A Combination of the Orthogonal Polynomials with Least – Squares Method for Solving High-Orders Fredholm-Volterra Integro-Differential Equations

This study introduced new technique which is based on a combination of the least-squares technique (LST) with Chebyshev and Legendre polynomials for finding the approximate solutions of higher-order linear Fredholm-Volterra integro-differential equations (FVIDEs) subject to the mixed conditions. Two examples of second and third-order linear FVIDEs are considered to illustrate the proposed method, the numerical results are comprised to demonstrate the validity and applicability of this technique, and comparisons with the exact solution are made. These results have shown that the competence and accuracy of the present technique.