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Article

Taylor Collocation Method for Solving a Class of the First Order Nonlinear Differential Equations

by
Dilek Taştekin
*,
Salih Yalçınbaş
* and
Mehmet Sezer
*
Department of Mathematics, Celal Bayar University, 45140, Muradiye, Manisa, Turkey
*
Authors to whom correspondence should be addressed.
Math. Comput. Appl. 2013, 18(3), 383-391; https://doi.org/10.3390/mca18030383
Published: 1 December 2013
Versions Notes

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

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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. https://doi.org/10.3390/mca18030383

AMA Style

Taştekin D, Yalçınbaş S, Sezer M. Taylor Collocation Method for Solving a Class of the First Order Nonlinear Differential Equations. Mathematical and Computational Applications. 2013; 18(3):383-391. https://doi.org/10.3390/mca18030383

Chicago/Turabian Style

Taştekin, Dilek, Salih Yalçınbaş, and Mehmet Sezer. 2013. "Taylor Collocation Method for Solving a Class of the First Order Nonlinear Differential Equations" Mathematical and Computational Applications 18, no. 3: 383-391. https://doi.org/10.3390/mca18030383

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