Abstract
Tensor-product formulae based on one-dimensional Gaussian quadratures are developed for evaluating double integrals of the type indicated in the title. If the singularities occur only along the diagonal and the regular part of the integrand is a polynomial of total degree d, the formulae can be made exact by choosing the number of quadrature points larger than, or equal to, 1 + d/2. Numerical examples are given as well as an application to a problem in aerodynamics.
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Dedicated to Claude Brezinski and Sebastiano Seatzu on the occasion of their 70th birthdays.
An erratum to this article is available at http://dx.doi.org/10.1007/s11075-013-9787-7.
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Gautschi, W. Numerical integration over the square in the presence of algebraic/logarithmic singularities with an application to aerodynamics. Numer Algor 61, 275–290 (2012). https://doi.org/10.1007/s11075-012-9611-9
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DOI: https://doi.org/10.1007/s11075-012-9611-9
Keywords
- Numerical integration over the square
- Algebraic/logarithmic singular lines along the diagonal and the sides of the square
- Gaussian quadrature
- Aerodynamical drag coefficient