M ¨untz-legendre matrix method to solve the delay fredholm integro-differential equations with constant coefficients

Abstract

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