Direct solution of second-order system of ODEs using Bernstein polynomials on an arbitrary interval

In this paper, we propose a direct method based on the Bernstein polynomials for solving systems of second-order ordinary differential equations (ODEs) on an arbitrary interval. This method gives numerical solutions by converting the ODE system into a system of algebraic equations which can be solved easily. The approximate solutions are given in series form. Some numerical examples are given to show the applicability of the method.