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Mathematical and Computational Applications is published by MDPI from Volume 21 Issue 1 (2016). Previous articles were published by another publisher in Open Access under a CC-BY (or CC-BY-NC-ND) licence, and they are hosted by MDPI on mdpi.com as a courtesy and upon agreement with Association for Scientific Research (ASR).
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Article

Legendre Series Solutions of Fredholm Integral Equations

by
Salih Yalçınbas
*,
Müge Aynigül
and
Tuğçe Akkaya
Department of Mathematics, Faculty of Science and Arts , Celal Bayar University Muradiye, Manisa, Turkey
*
Author to whom correspondence should be addressed.
Math. Comput. Appl. 2010, 15(3), 371-381; https://doi.org/10.3390/mca15030371
Published: 1 December 2010
Versions Notes

Abstract

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

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MDPI and ACS Style

Yalçınbas, S.; Aynigül, M.; Akkaya, T. Legendre Series Solutions of Fredholm Integral Equations. Math. Comput. Appl. 2010, 15, 371-381. https://doi.org/10.3390/mca15030371

AMA Style

Yalçınbas S, Aynigül M, Akkaya T. Legendre Series Solutions of Fredholm Integral Equations. Mathematical and Computational Applications. 2010; 15(3):371-381. https://doi.org/10.3390/mca15030371

Chicago/Turabian Style

Yalçınbas, Salih, Müge Aynigül, and Tuğçe Akkaya. 2010. "Legendre Series Solutions of Fredholm Integral Equations" Mathematical and Computational Applications 15, no. 3: 371-381. https://doi.org/10.3390/mca15030371

APA Style

Yalçınbas, S., Aynigül, M., & Akkaya, T. (2010). Legendre Series Solutions of Fredholm Integral Equations. Mathematical and Computational Applications, 15(3), 371-381. https://doi.org/10.3390/mca15030371

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