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Mathematics of Computation

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Quadrature of integrands with a logarithmic singularity


Author: John A. Crow
Journal: Math. Comp. 60 (1993), 297-301
MSC: Primary 65D32; Secondary 65D30
DOI: https://doi.org/10.1090/S0025-5718-1993-1155572-3
MathSciNet review: 1155572
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Abstract: A quadrature rule is presented that is exact for integrands of the form $ \pi (\xi ) + \varpi (\xi )\log \xi $ on the interval (0, 1), where $ \pi $ and $ \varpi $ are polynomials. The computed weights and abscissae are given for one- through seven-point rules. In particular, the four-point rule is exact for integral operators with log-arithmically singular kernel on a cubic B-spline basis, and it is expected these results shall prove useful for numerical applications of weighted-residual finite element methods.


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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1993-1155572-3
Keywords: Numerical integration, quadrature formula, Galerkin method
Article copyright: © Copyright 1993 American Mathematical Society