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Article

Bernstein Collocation Method for Solving the First Order Nonlinear Differential Equations with the Mixed Non-Linear Conditions

by
Salih Yalçınbaş
* and
Huriye Gürler
*
Department of Mathematics, Celal Bayar University, 45140, Muradiye, Manisa, Turkey
*
Authors to whom correspondence should be addressed.
Math. Comput. Appl. 2015, 20(3), 160-173; https://doi.org/10.3390/mca20010173
Published: 1 December 2015
Versions Notes

Abstract

In this study, we present the Bernstein matrix method to solve the first order nonlinear ordinary differential equations with the mixed non-linear conditions. By using this method, we obtain the approximate solutions in form of the Bernstein polynomials [1,2,16,17]. The method reduces the problem to a system of the nonlinear algebraic equations by means of the required matrix relations of the solutions form. By solving this system, the approximate solution is obtained. Finally, the method will be illustrated on the examples.
Keywords: nonlinear ordinary differential equations; riccati equation; Bernstein polynomials; collocation points nonlinear ordinary differential equations; riccati equation; Bernstein polynomials; collocation points

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MDPI and ACS Style

Yalçınbaş, S.; Gürler, H. Bernstein Collocation Method for Solving the First Order Nonlinear Differential Equations with the Mixed Non-Linear Conditions. Math. Comput. Appl. 2015, 20, 160-173. https://doi.org/10.3390/mca20010173

AMA Style

Yalçınbaş S, Gürler H. Bernstein Collocation Method for Solving the First Order Nonlinear Differential Equations with the Mixed Non-Linear Conditions. Mathematical and Computational Applications. 2015; 20(3):160-173. https://doi.org/10.3390/mca20010173

Chicago/Turabian Style

Yalçınbaş, Salih, and Huriye Gürler. 2015. "Bernstein Collocation Method for Solving the First Order Nonlinear Differential Equations with the Mixed Non-Linear Conditions" Mathematical and Computational Applications 20, no. 3: 160-173. https://doi.org/10.3390/mca20010173

APA Style

Yalçınbaş, S., & Gürler, H. (2015). Bernstein Collocation Method for Solving the First Order Nonlinear Differential Equations with the Mixed Non-Linear Conditions. Mathematical and Computational Applications, 20(3), 160-173. https://doi.org/10.3390/mca20010173

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