On the Derivatives of Bernstein Polynomials: An Application for the Solution of High Even-Order Differential Equations. (15th March 2011)

• Record Type: Journal Article
• Authors: Doha, E. H.; Bhrawy, A. H.; Saker, M. A.
• Other Names: Messaoudi S. Academic Editor.
• Is Part Of: Boundary value problems. Volume 2011(2011)
• Publication Date: 2011-03-15
• Subjects: Boundary value problems -- Periodicals; Boundary value problems; Electronic journals; Periodicals; 515.35
• DOI: 10.1155/2011/829543
• Languages: English
• ISSNs: 1687-2762

Abstract

Abstract : A new formula expressing explicitly the derivatives of Bernstein polynomials of any degree and for any order in terms of Bernstein polynomials themselves is proved, and a formula expressing the Bernstein coefficients of the general-order derivative of a differentiable function in terms of its Bernstein coefficients is deduced. An application of how to use Bernstein polynomials for solving high even-order differential equations by Bernstein Galerkin and Bernstein Petrov-Galerkin methods is described. These two methods are then tested on examples and compared with other methods. It is shown that the presented methods yield better results.