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Mathematical and Computational Applications is published by MDPI from Volume 21 Issue 1 (2016). Articles in this Issue were published by another publisher in Open Access under a CC-BY (or CC-BY-NC-ND) licence. Articles are hosted by MDPI on as a courtesy and upon agreement with the previous journal publisher.
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Math. Comput. Appl. 2010, 15(3), 371-381;

Legendre Series Solutions of Fredholm Integral Equations

Department of Mathematics, Faculty of Science and Arts , Celal Bayar University Muradiye, Manisa, Turkey
Author to whom correspondence should be addressed.
Published: 1 December 2010
PDF [193 KB, uploaded 4 April 2016]


A matrix method for approximately solving linear Fredholm integral equations of the second kind is presented. The solution involves a truncated Legendre series approximation. The method is based on first taking the truncated Legendre series expansions of the functions in equation and then substituting their matrix forms into the equation. Thereby the equation reduces to a matrix equation, which corresponds to a linear system of algebraic equations with unknown Legendre coefficients. In addition, some equations considered by other authors are solved in terms of Legendre polynomials and the results are compared.
Keywords: Legendre series; Fredholm integral equations Legendre series; Fredholm integral equations
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Yalçınbas, S.; Aynigül, M.; Akkaya, T. Legendre Series Solutions of Fredholm Integral Equations. Math. Comput. Appl. 2010, 15, 371-381.

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