Bernstein Polynomial Collocation Method for Elliptic Boundary Value Problems |
| |
| Authors: | Nikola Mirkov Bo?ko Ra?uo |
| |
| Institution: | 1. University of Belgrade, Institute of Nuclear Sciences ‘Vinca’, Mike Alasa 12-14, Belgrade, Serbia;2. University of Belgrade, Faculty of Mechanical Engineering, Kraljice Marije 16, Belgrade, Serbia |
| |
| Abstract: | 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) |
| |
| Keywords: | |
|
|
