Hypersingular integral equations over a disc: convergence of a spectral method and connection with Tranter's method - Archive ouverte HAL Access content directly
Journal Articles Journal of Computational and Applied Mathematics Year : 2014

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

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Abstract

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.
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Dates and versions

hal-00971497 , version 1 (06-07-2015)

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Leandro Farina, Paul A. Martin, Victor Péron. Hypersingular integral equations over a disc: convergence of a spectral method and connection with Tranter's method. Journal of Computational and Applied Mathematics, 2014, 269, pp.118-131. ⟨10.1016/j.cam.2014.03.014⟩. ⟨hal-00971497⟩
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