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Math. Comput. Appl. 2015, 20(3), 160-173; doi:10.3390/mca20010173

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

Department of Mathematics, Celal Bayar University, 45140, Muradiye, Manisa, Turkey
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Published: 1 December 2015
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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
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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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.

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Math. Comput. Appl. EISSN 2297-8747 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
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