Numerical solutions of systems of high-order Fredholm integro-differential equations using Euler polynomials

In this paper, a novel method called Euler collocation method is presented to obtain an approximate solution for systems of high-order Fredholm integro-differential equations. The most significant features of this method are its simplicity and excellent accuracy. After implementation of our method, the main problem would be transformed into a system of algebraic equations such that its solutions are the unknown Euler coefficients. In addition, under several mild conditions the error and stability analysis of the proposed method are discussed. Finally, complete comparisons with other methods and superior results confirm the validity and applicability of the presented method.