Müntz-Legendre Polynomıal Solutıons of Lınear Delay Fredholm Integro-Dıfferentıal Equatıons And Resıdual Correctıon

Abstract

In this paper, we consider the Mü ntz-Legendre polynomial solutions of the linear delay Fredholm integro-differential equations and residual correction. Firstly, the linear delay Fredholm integro-differential equations are transformed into a system of linear algebraic equations by using by the matrix operations of the Mü ntz-Legendre polynomials and the collocation points. When this system is solved, the Mü ntzLegendre polynomial solution is obtained. Then, an error estimation is presented by means of the residual function and the Mü ntz-Legendre polynomial solutions are improved by the residual correction method. The technique is illustrated by studying the problem for an example. The obtained results show that error estimation and the residual correction method is very effective.