A new algorithm for the numerical solution of the first order nonlinear differential equations with the mixed non-linear conditions by using bernstein polynomials

In this study, an approximate method based on Bernstein polynomials has been presented to obtain the solution first order nonlinear ordinary differential equations with the mixed non-linear conditions. The method by means of Bernstein collocation points, transforms the differential equation to a matrix equation which corresponds to a system of nonlinear algebraic equations with unknown Bernstein coefficients in [1, 2]. The method can be used for solving Riccati equation as well. The numerical results show the applicability of the method for this type of equations. Comparisons are made between the obtained solution and the exact solution.