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 on the interval (0, 1), where and 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