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Bernstein Polynomial Collocation Method for Elliptic Boundary Value Problems
Author(s) -
Mirkov Nikola,
Rašuo Boško
Publication year - 2013
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201310206
Subject(s) - chebyshev pseudospectral method , mathematics , pseudospectral optimal control , chebyshev polynomials , legendre polynomials , chebyshev nodes , interpolation (computer graphics) , bernstein polynomial , polynomial , collocation (remote sensing) , mathematical analysis , convergence (economics) , gauss pseudospectral method , chebyshev filter , boundary value problem , orthogonal polynomials , pseudo spectral method , classical orthogonal polynomials , chebyshev equation , computer science , fourier transform , animation , fourier analysis , computer graphics (images) , machine learning , economics , economic growth
We present a summary of recent developments in application of Bernstein polynomials to solution of elliptic boundary value problems with a pseudospectral method. Solution is approximated using Benstein polynomial interpolant defined at points of the extrema of Chebyshev polynomials i.e. the Chebyshev‐Gauss‐Lobatto (CGL) nodes. This approach brings impovement comparing to the Bernstein interpolation at equidistant nodes we used previously [1]. We show that this approach leads to spectral convergence and accuracy comparable to that of pseudospectral methods with orthogonal polynomials (Chebyshev, Legendre). The algorithm is implemented in open source library bernstein‐poly , which is available online. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)