A Taylor polynomial approach for solving high-order linear Fredholm integro-differential equations in the most general form

Abstract

A Taylor method is developed for finding the approximate solution of high-order linear Fredholm integro-differential equations in the most general form under the mixed conditions. The problem is defined on the interval [-1,1] and the solution is obtained in terms of Taylor polynomials about the origin. Transforming the interval [a, b] to the interval [-1, 1], a problem defined on [a, b] can also be solved using this method. Numerical examples are presented to illustrate the accuracy of the method.