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Math. Comput. Appl. 2013, 18(3), 476-485; doi:10.3390/mca18030476

Müntz-Legendre Polynomial Solutions of Linear Delay Fredholm Integro-Differential Equations and Residual Correction

1
Department of Mathematics, Faculty of Science, Akdeniz University, 07058, Antalya, Turkey
2
Department of Mathematics, Faculty of Science, Muğla Sıtkı Koçman University, 48000, Muğla, Turkey
3
Department of Mathematics, Faculty of Science, Celal Bayar University, 45000, Manisa, Turkey
*
Author to whom correspondence should be addressed.
Published: 1 December 2013
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Abstract

In this paper, we consider the Müntz-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 Müntz-Legendre polynomials and the collocation points. When this system is solved, the Müntz- Legendre polynomial solution is obtained. Then, an error estimation is presented by means of the residual function and the Müntz-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.
Keywords: Linear delay Fredholm integro-differential equation; Müntz-Legendre polynomials; collocation method; residual function Linear delay Fredholm integro-differential equation; Müntz-Legendre polynomials; collocation method; residual function
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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MDPI and ACS Style

Yüzbaşı, Ş.; Gök, E.; Sezer, M. Müntz-Legendre Polynomial Solutions of Linear Delay Fredholm Integro-Differential Equations and Residual Correction. Math. Comput. Appl. 2013, 18, 476-485.

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Math. Comput. Appl. EISSN 2297-8747 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
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