Numerical integration over a disc. A new Gaussian quadrature formula

Summary.

We construct a quadrature formula for integration on the unit disc which is based on line integrals over \(n\) distinct chords in the disc and integrates exactly all polynomials in two variables of total degree \(2n-1\).

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Authors and Affiliations

1. Department of Mathematics, University of Sofia, Blvd. James Boucher 5, 1126 Sofia, Bulgaria, e-mail: bor@bgearn.acad.bg , , , , , , BG

   Borislav Bojanov

2. Department of Mathematics, University of South Carolina, Columbia, SC 29208, USA, e-mail: petrova@math.sc.edu , , , , , , US

   Guergana Petrova

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1. Borislav Bojanov
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2. Guergana Petrova
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Received August 8, 1996 / Revised version received July 2, 1997

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Bojanov, B., Petrova, G. Numerical integration over a disc. A new Gaussian quadrature formula. Numer. Math. 80, 39–59 (1998). https://doi.org/10.1007/s002110050358

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• Issue Date: July 1998

• DOI: https://doi.org/10.1007/s002110050358

• Mathematics Subject Classification (1991): 65D32, 65D30, 41A55