On the Derivatives of Bernstein Polynomials: An Application for the Solution of High Even-Order Differential Equations
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Date
2011
Authors
Journal Title
Journal ISSN
Volume Title
Type
Article
Publisher
SPRINGER
Series Info
BOUNDARY VALUE PROBLEMS;Article Number: 829543
Scientific Journal Rankings
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