Integrals of Bernstein polynomials: An application for the solution of high even-order differential equations

A new explicit formula for the integrals of Bernstein polynomials of any degree for any order in terms of Bernstein polynomials themselves is derived. A fast and accurate algorithm is developed for the solution of high even-order boundary value problems (BVPs) with two point boundary conditions but...

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Bibliographic Details
Published in:Applied mathematics letters 2011-04, Vol.24 (4), p.559-565
Main Authors: Doha, E.H., Bhrawy, A.H., Saker, M.A.
Format: Article
Language:English
Subjects:
Algorithms
Bernstein polynomials
Boundary conditions
Boundary value problems
Construction
Differential equations
Exact sciences and technology
High order differential equations
Integrals
Mathematical analysis
Mathematical models
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Ordinary differential equations
Partial differential equations, boundary value problems
Sciences and techniques of general use
Spectral method
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Summary:A new explicit formula for the integrals of Bernstein polynomials of any degree for any order in terms of Bernstein polynomials themselves is derived. A fast and accurate algorithm is developed for the solution of high even-order boundary value problems (BVPs) with two point boundary conditions but by considering their integrated forms. The Bernstein–Petrov–Galerkin method (BPG) is applied to construct the numerical solution for such problems. The method is then tested on examples and compared with other methods. It is shown that the BPG yields better results.
ISSN:0893-9659
1873-5452
DOI:10.1016/j.aml.2010.11.013