An iterative approximate method of solving boundary value problems using dual Bernstein polynomials
Year: 2017
Type: preprint
Abstract: In this paper, we present a new iterative approximate method of solving boundary value problems. The idea is to compute approximate polynomial solutions in the Bernstein form using least squares approximation combined with some properties of dual Bernstein polynomials which guarantee high efficiency of our approach. The method can deal with both linear and nonlinear differential equations. Moreover, not only second order differential equations can be solved but also higher order differential equations. Illustrative examples confirm the versatility of our method.
Source: arXiv (Cornell University)
Authors: Gospodarczyk, Przemysław, Woźny, Paweł
Institution: University of Wrocław
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2752545646