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

Taştekin, Dilek; Yalçınbaş, Salih; Sezer, Mehmet

doi:10.3390/mca18030383

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Article

1 December 2013

9 Pages

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

and

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

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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

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