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S. Yalçınbaş and M. Sezer, The approximate solution of high-order linear Volterra–Fredholm integrodifferential equations in terms of Taylor polynomials, Applied Mathematics and Computation 112, 291-308, 2000.

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Article

Fermat Collocation Method for Solvıng a Class of the First Order Nonlinear Differential Equations

1Department of Mathematics Celal Bayar University, Muradiye, Manisa, Turkey


Journal of Mathematical Sciences and Applications. 2014, Vol. 2 No. 1, 4-9
DOI: 10.12691/jmsa-2-1-2
Copyright © 2014 Science and Education Publishing

Cite this paper:
Dilek Taştekin, Salih Yalçinbaş. Fermat Collocation Method for Solvıng a Class of the First Order Nonlinear Differential Equations. Journal of Mathematical Sciences and Applications. 2014; 2(1):4-9. doi: 10.12691/jmsa-2-1-2.

Correspondence to: Salih  Yalçinbaş, Department of Mathematics Celal Bayar University, Muradiye, Manisa, Turkey. Email: salih.yalcinbas@cbu.edu.tr

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 Fermat collocation method. The solution is obtained in the form of a truncated Fermat 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.

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