MÜNTZ-LEGENDRE POLYNOMIAL SOLUTIONS OF LINEAR DELAY FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS AND RESIDUAL CORRECTION

Emrah GÖK; Şuayip YÜZBAŞI; Mehmet SEZER

MÜNTZ-LEGENDRE POLYNOMIAL SOLUTIONS OF LINEAR DELAY FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS AND RESIDUAL CORRECTION

Date

2013

Authors

Emrah GÖK

Şuayip YÜZBAŞI

Mehmet SEZER

Abstract

In this paper, we consider the Müntz-Legendre polynomial solutions of thelinear delay Fredholm integro-differential equations and residual correction. Firstly, thelinear delay Fredholm integro-differential equations are transformed into a system oflinear algebraic equations by using by the matrix operations of the Müntz-Legendrepolynomials and the collocation points. When this system is solved, the MüntzLegendrepolynomial solution is obtained. Then, an error estimation is presented bymeans of the residual function and the Müntz-Legendre polynomial solutions areimproved by the residual correction method. The technique is illustrated by studying theproblem for an example. The obtained results show that error estimation and theresidual correction method is very effective.