Operational matrices of Bernstein polynomials and their applications

Abstract

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.

Keywords:

• Bernstein polynomial
• operational matrix
• differential equation

Acknowledgements

The authors wish to express their sincere thanks to the referees for their valuable suggestions that improved the final manuscript.