THE NUMERICAL SOLUTIONS OF INTEGRO-DIFFERENTIAL EQUATIONS BY EULER POLYNOMIALS WITH LEAST–SQUARES METHOD

Abstract

This study introduced a new technique based on the combination of the least-squares method (LSM) with Euler polynomials for finding the approximate solutions of integro-differential equations (IDEs) subject to the mixed conditions. Three examples of first and second-orders linear Fredholm IDEs (FIDEs) and Volterra IDEs (VIDEs) are considered to illustrate the proposed method. The numerical results comprised to demonstrate the validity and applicability of this method comparisons with the exact solution shown that the competence and accuracy of the present technique.