Operational matrices of Bernstein polynomials and their applications

The Bernstein polynomials (B-polynomials) operational matrices of integration P, differentiation D and product Ĉ are derived. A general procedure of forming these matrices are given. These matrices can be used to solve problems such as calculus of variations, differential equations, optimal control and integral equations. Illustrative examples are included to demonstrate the validity and applicability of the operational matrices.