Hypersingular integral equations over a disc: Convergence of a spectral method and connection with Tranter's method

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:269

Article

Farina, Leandro^1,2  Martin, P. A.³  Peron, Victor⁴ 

[1] Univ Fed Rio Grande do Sul, Inst Matemat, Porto Alegre, RS, Brazil

[2] BCAM, Bilbao, Basque County, Spain

[3] Colorado Sch Mines, Dept Appl Math & Stat, Golden, CO 80401 USA

[4] Univ Pau & Pays Adour, MAGIQUE3D, INRIA Bordeaux Sud Ouest, LMA, F-64013 Pau, France

关键词: Hypersingular integral equations;    Spectral method;    Galerkin method;    Tranter's method;    Jacobi polynomials;    Screen problems;   

DOI  :  10.1016/j.cam.2014.03.014

来源: Elsevier

【 摘 要 】

Two-dimensional hypersingular equations over a disc are considered. A spectral method is developed, using Fourier series in the azimuthal direction and orthogonal polynomials in the radial direction. The method is proved to be convergent. Then, Tranter's method is discussed. This method was devised in the 1950s to solve certain pairs of dual integral equations. It is shown that this method is also convergent because it leads to the same algebraic system as the spectral method. (c) 2014 Elsevier B.V. All rights reserved.

【 授权许可】

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