An efficient approach for the numerical solution of Fredholm Integro-differential equations

In this paper, we consider the collocation approach for the numerical solution of Fredholm integro-differential equations using power series polynomial as our basis function. After obtaining an integral representation of the problem, we used standard collocation points to transform the problem into a system of linear algebraic equations. We adopted the matrix inversion method to solve the algebraic equation and substituted the result of the algebraic into the approximate solution to obtain the numerical result. Some numerical problems are solved to show the method's efficiency and consistency.