Error bounds for compound quadrature of weakly singular integrals
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- by Alan Feldstein and Richard K. Miller PDF
- Math. Comp. 25 (1971), 505-520 Request permission
Abstract:
This paper studies the convergence of numerical quadratures of singular integrands. The singularities are ignored in the sense that whenever a singularity occurs the integrand is redefined to be zero. Several convergence theorems are proved under the assumption that the integrand can be dominated near each singularity by a monotone, integrable function.References
- Arthur Sard, Linear approximation, American Mathematical Society, Providence, R.I., 1963. MR 0158203
- A. H. Stroud, Estimating quadrature errors for functions with low continuity, SIAM J. Numer. Anal. 3 (1966), 420–424. MR 215528, DOI 10.1137/0703036
- Philip J. Davis and Philip Rabinowitz, Ignoring the singularity in approximate integration, J. Soc. Indust. Appl. Math. Ser. B Numer. Anal. 2 (1965), 367–383. MR 195256
- Philip Rabinowitz, Gaussian integration in the presence of a singularity, SIAM J. Numer. Anal. 4 (1967), 191–201. MR 213016, DOI 10.1137/0704018
- Walter Gautschi, Numerical quadrature in the presence of a singularity, SIAM J. Numer. Anal. 4 (1967), 357–362. MR 218014, DOI 10.1137/0704031
- L. Fox, Romberg integration for a class of singular integrands, Comput. J. 10 (1967), 87–93. MR 213013, DOI 10.1093/comjnl/10.1.87
- Philip J. Davis and Philip Rabinowitz, Numerical integration, Blaisdell Publishing Co. [Ginn and Co.], Waltham, Mass.-Toronto, Ont.-London, 1967. MR 0211604
- Eugene Isaacson and Herbert Bishop Keller, Analysis of numerical methods, John Wiley & Sons, Inc., New York-London-Sydney, 1966. MR 0201039
- Kendall E. Atkinson, The numerical solution of Fredholm integral equations of the second kind, SIAM J. Numer. Anal. 4 (1967), 337–348. MR 224314, DOI 10.1137/0704029 D. G. Schweikert, Numerical Parametric Integration of Continuous Functions with a Singular Derivative, Proc. Twenty-Third National Conference of A.C.M., Brandon Systems Press, Princeton, N.J., 1968.
- R. K. Miller, On ignoring the singularity in numerical quadrature, Math. Comp. 25 (1971), 521–532. MR 301901, DOI 10.1090/S0025-5718-1971-0301901-5 A. Erdélyi (Editor), Higher Transcendental Functions. Vol. 2, McGraw-Hill, New York, 1953. MR 15, 419.
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Math. Comp. 25 (1971), 505-520
- MSC: Primary 65D30
- DOI: https://doi.org/10.1090/S0025-5718-1971-0297127-4
- MathSciNet review: 0297127