Hypersingular integral equations over a disc: Convergence of a spectral method and connection with Tranter's method
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 dev...
| Authors: | , , |
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| Format: | article |
| Status: | Published version |
| Publication Date: | 2014 |
| Country: | España |
| Institution: | Basque Center for Applied Mathematics (BCAM) |
| Repository: | BIRD. BCAM's Institutional Repository Data |
| OAI Identifier: | oai:bird.bcamath.org:20.500.11824/92 |
| Online Access: | http://hdl.handle.net/20.500.11824/92 |
| Access Level: | Open access |
| Keyword: | Fourier series Galerkin methods Integral equations Polynomials Azimuthal direction Dual integral equations Hypersingular equation Hypersingular integral equation Jacobi polynomials Orthogonal polynomial Spectral methods Tranter's method Spectroscopy |
| Summary: | 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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