Boundary Galerkin Method of a Skew-Derivative Problem in the Exterior of an Open Arc Based on Chebyshev Polynomials. (17th March 2013)

• Record Type: Journal Article
• Authors: Sun, Wei; Ma, Fuming
• Other Names: Gendelman Oleg V. Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2013(2013)
• Publication Date: 2013-03-17
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2013/354267
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : 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.