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Journal of Applied Mathematics
Volume 2012 (2012), Article ID 859315, 11 pages
http://dx.doi.org/10.1155/2012/859315
Research Article

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

School of Mathematics and Statistics, Central South University, Changsha 410083, China

Received 10 June 2012; Accepted 11 August 2012

Academic Editor: Francisco J. Marcellán

Copyright © 2012 Jiankang Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.