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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 354267, 9 pages
Research Article

Boundary Galerkin Method of a Skew-Derivative Problem in the Exterior of an Open Arc Based on Chebyshev Polynomials

Wei Sun1,2 and Fuming Ma1

1School of Mathematics, Jilin University, Changchun 130012, China
2Harbin University of Science and Technology, Harbin 150080, China

Received 14 December 2012; Accepted 23 January 2013

Academic Editor: Oleg V. Gendelman

Copyright © 2013 Wei Sun and Fuming Ma. 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.


A problem modeling Hall effect in a semiconductor film from an electrode of arbitrary shape is considered, which is a skew-derivative problem. Boundary Galerkin method for solving the problem in Sobolev spaces is developed firstly. The solution is represented in the form of the combined angular potential and single-layer potential. The final integral equations do not contain hypersingular integrals. Uniqueness and existence of the solution to the equations are proved. The weakly singular and Cauchy singular integral arising in these equations can be computed directly by truncated series of Chebyshev polynomials with their weighting function without approximation. The numerical simulation showing the high accuracy of the scheme is presented.