Journal of Applied Mathematics

Bernstein-Polynomials-Based Highly Accurate Methods for One-Dimensional Interface Problems

Jiankang Liu, Zhoushun Zheng, and Qinwu Xu

Full-text: Open access

Abstract

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.

Article information

Source
J. Appl. Math., Volume 2012 (2012), Article ID 859315, 11 pages.

Dates
First available in Project Euclid: 14 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.jam/1355495290

Digital Object Identifier
doi:10.1155/2012/859315

Mathematical Reviews number (MathSciNet)
MR2970427

Zentralblatt MATH identifier
1251.65139

Citation

Liu, Jiankang; Zheng, Zhoushun; Xu, Qinwu. Bernstein-Polynomials-Based Highly Accurate Methods for One-Dimensional Interface Problems. J. Appl. Math. 2012 (2012), Article ID 859315, 11 pages. doi:10.1155/2012/859315. https://projecteuclid.org/euclid.jam/1355495290


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