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Math. Comput. Appl. 2013, 18(3), 383-391; doi:10.3390/mca18030383

Taylor Collocation Method for Solving a Class of the First Order 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, we present a reliable numerical approximation of the some first order nonlinear ordinary differential equations with the mixed condition by the using a new Taylor collocation method. The solution is obtained in the form of a truncated Taylor series with easily determined components. Also, the method can be used to solve Riccati equation. The numerical results show the effectuality of the method for this type of equations. Comparing the methodology with some known techniques shows that the existing approximation is relatively easy and highly accurate.
Keywords: Nonlinear ordinary differential equations; Riccati equation; Taylor polynomials; collocation points Nonlinear ordinary differential equations; Riccati equation; Taylor polynomials; collocation points
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

Taştekin, D.; Yalçınbaş, S.; Sezer, M. Taylor Collocation Method for Solving a Class of the First Order Nonlinear Differential Equations. Math. Comput. Appl. 2013, 18, 383-391.

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