Müntz-Legendre Matrix Method to solve Delay Fredholm Integro-Differential Equations with constant coefficients

In this study, we present the Müntz-Legendre matrix method to solve the linear delay Fredholm integro-differential equations with constant coeffcients. By using this method, we obtain the approximate solutions in form of the Müntz-Legendre polynomials. The method reduces the problem to a system of the algebraic equations by means of the required matrix relations of the solution form. By solving this system, the approximate solution is obtained. Also, an error estimation scheme based the residual function is presented for the method and the approximate solutions are improved by this error estimation. Finally, the method will be illustrated on the examples.