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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 Collocation Method for Solving Nonlinear Differential Equations

by
Aysun Güner
* and
Salih Yalçınbaş
Department of Mathematics, Celal Bayar University, 45140, Muradiye, Manisa, Turkey
*
Author to whom correspondence should be addressed.
Math. Comput. Appl. 2013, 18(3), 521-530; https://doi.org/10.3390/mca18030521
Published: 1 December 2013
Versions Notes

Abstract

In this study, a matrix method based on Legendre collocation points on interval [-1,1] is proposed for the approximate solution of the some first order nonlinear ordinary differential equations with the mixed conditions in terms of Legendre polynomials. The method by means of Legendre collocation points, transforms the differential equation to a matrix equation which corresponds to a system of nonlinear algebraic equations with unknown Legendre coefficients. Also, the method can be used for solving Riccati equation. The numerical results show the effectuality of the method for this type of equations. Comparisons are made between the obtained solution and the exact solution.
Keywords: Nonlinear ordinary differential equations; Legendre polynomials and series; Legendre collocation points; Legendre collocation method Nonlinear ordinary differential equations; Legendre polynomials and series; Legendre collocation points; Legendre collocation method

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MDPI and ACS Style

Güner, A.; Yalçınbaş, S. Legendre Collocation Method for Solving Nonlinear Differential Equations. Math. Comput. Appl. 2013, 18, 521-530. https://doi.org/10.3390/mca18030521

AMA Style

Güner A, Yalçınbaş S. Legendre Collocation Method for Solving Nonlinear Differential Equations. Mathematical and Computational Applications. 2013; 18(3):521-530. https://doi.org/10.3390/mca18030521

Chicago/Turabian Style

Güner, Aysun, and Salih Yalçınbaş. 2013. "Legendre Collocation Method for Solving Nonlinear Differential Equations" Mathematical and Computational Applications 18, no. 3: 521-530. https://doi.org/10.3390/mca18030521

APA Style

Güner, A., & Yalçınbaş, S. (2013). Legendre Collocation Method for Solving Nonlinear Differential Equations. Mathematical and Computational Applications, 18(3), 521-530. https://doi.org/10.3390/mca18030521

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