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Volume 6, Issue 3
Quadrature Formulas for Singular Integrals with Hilbert Kernel

Jin-Yuan Du

J. Comp. Math., 6 (1988), pp. 205-225.

Published online: 1988-06

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  • Abstract

In this paper, we first establish the quadrature formulae of proper integrals with weight by trigonometric interpolation. Then we use the method of separation of singularity to derive the quadrature formulae of corresponding singular integrals with Hilbert Kernel. The trigonometric precision, the estimate of the remainder and the convergence of each quadrature formula derived here are also established.

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@Article{JCM-6-205, author = {Jin-Yuan Du}, title = {Quadrature Formulas for Singular Integrals with Hilbert Kernel}, journal = {Journal of Computational Mathematics}, year = {1988}, volume = {6}, number = {3}, pages = {205--225}, abstract = {

In this paper, we first establish the quadrature formulae of proper integrals with weight by trigonometric interpolation. Then we use the method of separation of singularity to derive the quadrature formulae of corresponding singular integrals with Hilbert Kernel. The trigonometric precision, the estimate of the remainder and the convergence of each quadrature formula derived here are also established.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9511.html} }
TY - JOUR T1 - Quadrature Formulas for Singular Integrals with Hilbert Kernel AU - Jin-Yuan Du JO - Journal of Computational Mathematics VL - 3 SP - 205 EP - 225 PY - 1988 DA - 1988/06 SN - 6 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9511.html KW - AB -

In this paper, we first establish the quadrature formulae of proper integrals with weight by trigonometric interpolation. Then we use the method of separation of singularity to derive the quadrature formulae of corresponding singular integrals with Hilbert Kernel. The trigonometric precision, the estimate of the remainder and the convergence of each quadrature formula derived here are also established.

Jin-Yuan Du. (1988). Quadrature Formulas for Singular Integrals with Hilbert Kernel. Journal of Computational Mathematics. 6 (3). 205-225. doi:
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