On the Derivatives of Bernstein Polynomials: An Application for the Solution of High Even-Order Differential Equations

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Date

2011

Journal Title

Journal ISSN

Volume Title

Type

Article

Publisher

SPRINGER

Series Info

BOUNDARY VALUE PROBLEMS;Article Number: 829543

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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.

Description

Accession Number: WOS:000296324600001

Keywords

University for BOUNDARY-VALUE-PROBLEMS, SPECTRAL-GALERKIN ALGORITHMS, CONNECTION COEFFICIENTS, RECURRENCE RELATIONS, ACOBI-POLYNOMIALS, ORTHOGONAL POLYNOMIALS, SPLINE SOLUTIONS, EXPANSIONS, SERIES

Citation

Cited References in Web of Science Core Collection: 24