Doha, E. H.Bhrawy, A. H.Saker, M. A.2019-11-182019-11-182011Cited References in Web of Science Core Collection: 241687-2770https://doi.org/10.1155/2011/829543https://link.springer.com/article/10.1155/2011/829543Accession Number: WOS:000296324600001A 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.enUniversity for BOUNDARY-VALUE-PROBLEMSSPECTRAL-GALERKIN ALGORITHMSCONNECTION COEFFICIENTSRECURRENCE RELATIONSACOBI-POLYNOMIALSORTHOGONAL POLYNOMIALSSPLINE SOLUTIONSEXPANSIONSSERIESArticlehttps://doi.org/10.1155/2011/829543