Bernstein-polynomials-based highly accurate methods for one-dimensional interface problems
type: Item
instance of: scholarly article
title: Bernstein-polynomials-based highly accurate methods for one-dimensional interface problems
zbMATH Open document ID: 1251.65139
DOI: 10.1155/2012/859315
author: Qinwu Xu
author: Jiankang Liu
author: Zhoushun Zheng
published in: Journal of Applied Mathematics
publication date: 2012-11-15T00:00:00Z
review text: Summary: A new numerical method based on Bernstein polynomials expansion is proposed for solving one-dimensional elliptic interface problems. Both Galerkin formulation and collocation formulation are constructed to determine the expansion coefficients. In Galerkin formulation, the flux jump condition can be imposed by the weak formulation naturally. In collocation formulation, the results obtained by B-polynomials expansion are compared with that obtained by Lagrange basis expansion. Numerical experiments show that B-polynomials expansion is superior to Lagrange expansion in both condition number and accuracy. Both methods can yield high accuracy even with small value of \(N\).
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 41A17
zbMATH DE Number: 6106330
zbMATH Keywords: Bernstein polynomials expansion
zbMATH Keywords: one-dimensional elliptic interface problems
zbMATH Keywords: Galerkin formulation
zbMATH Keywords: collocation formulation
Wikidata QID: Q58907494
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/859315
OpenAlex ID: W2161753342
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description: scientific article; zbMATH DE number 6106330