Quadrature over the sphere (Q2388707)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Quadrature over the sphere |
scientific article |
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Quadrature over the sphere (English)
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19 September 2005
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The paper is devoted to study a quadrature rule over the sphere, when the integrand has a singular behaviour in a polar region. The important idea of authors is to express the integrand in spherical coordinates. This transformation uses a grading parameter \(q\). Next the tapezoidal rule in spherical coordinates is applied and the convergence of the obtained quadrature formula is studied in the following cases: (i) \(2q\) is not an integer; (ii) \(2q\) is an odd integer. In the first case the asymptotic behaviour of the remainder term of quadratue formula is studied while in the second the convergence of the method is proved.
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spherical integration
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trapezoidal rule
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Euler-MacLaurin representation
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quadrature rule
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convergence
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asymptotic behaviour
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remainder term
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