Yalçinbaş S.Görler H.2024-07-222024-07-2220151300686Xhttp://akademikarsiv.cbu.edu.tr:4000/handle/123456789/16494In 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.EnglishAlgebraDifferential equationsMatrix algebraOrdinary differential equationsPolynomialsRiccati equationsApproximate solutionBernstein polynomialCollocation methodCollocation pointsFirst order nonlinear differential equationsNon-linear conditionsNonlinear algebraic equationsNonlinear ordinary differential equationNonlinear equationsArticle10.19029/mca-2015-014