Quadrature of integrands with a logarithmic singularity
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- by John A. Crow PDF
- Math. Comp. 60 (1993), 297-301 Request permission
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.References
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Additional Information
- © Copyright 1993 American Mathematical Society
- 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