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Math. Comput. Appl. 2013, 18(3), 521-530; doi:10.3390/mca18030521

Legendre Collocation Method for Solving Nonlinear Differential Equations

Department of Mathematics, Celal Bayar University, 45140, Muradiye, Manisa, Turkey
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Published: 1 December 2013
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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
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

Güner, A.; Yalçınbaş, S. Legendre Collocation Method for Solving Nonlinear Differential Equations. Math. Comput. Appl. 2013, 18, 521-530.

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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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