Operational matrices of orthonormal Bernstein polynomials and its application for solving differential equations

In this paper, an efficient approach is applied for numerical approximation of the ordinary differential equations based on operational matrices with respect to orthonormal Bernstein polynomials (OBPs). Firstly, operational matrices of integration and product of the OBPs are derived. Using this operational matrices for solving differential equations, we obtain a system of linear algebraic equations. Numerical results over some test problems indicate the superiority of the new method