Further convergence results for two quadrature rules for Cauchy type principal value integrals

Nikolaos I. Ioakimidis

Aplikace matematiky (1982)

  • Volume: 27, Issue: 6, page 457-466
  • ISSN: 0862-7940

Abstract

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New convergence and rate-of-convergence results are established for two well-known quadrature rules for the numerical evaluation of Cauchy type principal value integrals along a finite interval, namely the Gauss quadrature rule and a similar interpolatory quadrature rule where the same nodes as in the Gauss rule are used. The main result concerns the convergence of the interpolatory rule for functions satisfying the Hölder condition with exponent less or equal to 1 2 . The results obtained here supplement a series of previous results on the convergence of the aforementioned quadrature rules.

How to cite

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Ioakimidis, Nikolaos I.. "Further convergence results for two quadrature rules for Cauchy type principal value integrals." Aplikace matematiky 27.6 (1982): 457-466. <http://eudml.org/doc/15266>.

@article{Ioakimidis1982,
abstract = {New convergence and rate-of-convergence results are established for two well-known quadrature rules for the numerical evaluation of Cauchy type principal value integrals along a finite interval, namely the Gauss quadrature rule and a similar interpolatory quadrature rule where the same nodes as in the Gauss rule are used. The main result concerns the convergence of the interpolatory rule for functions satisfying the Hölder condition with exponent less or equal to $\frac\{1\}\{2\}$. The results obtained here supplement a series of previous results on the convergence of the aforementioned quadrature rules.},
author = {Ioakimidis, Nikolaos I.},
journal = {Aplikace matematiky},
keywords = {rate-of-convergence; quadrature rules; Cauchy type principal value integrals; finite interval; Gauss quadrature; interpolatory quadrature; rate-of-convergence; quadrature rules; Cauchy type principal value integrals; finite interval; Gauss quadrature; interpolatory quadrature},
language = {eng},
number = {6},
pages = {457-466},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Further convergence results for two quadrature rules for Cauchy type principal value integrals},
url = {http://eudml.org/doc/15266},
volume = {27},
year = {1982},
}

TY - JOUR
AU - Ioakimidis, Nikolaos I.
TI - Further convergence results for two quadrature rules for Cauchy type principal value integrals
JO - Aplikace matematiky
PY - 1982
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 27
IS - 6
SP - 457
EP - 466
AB - New convergence and rate-of-convergence results are established for two well-known quadrature rules for the numerical evaluation of Cauchy type principal value integrals along a finite interval, namely the Gauss quadrature rule and a similar interpolatory quadrature rule where the same nodes as in the Gauss rule are used. The main result concerns the convergence of the interpolatory rule for functions satisfying the Hölder condition with exponent less or equal to $\frac{1}{2}$. The results obtained here supplement a series of previous results on the convergence of the aforementioned quadrature rules.
LA - eng
KW - rate-of-convergence; quadrature rules; Cauchy type principal value integrals; finite interval; Gauss quadrature; interpolatory quadrature; rate-of-convergence; quadrature rules; Cauchy type principal value integrals; finite interval; Gauss quadrature; interpolatory quadrature
UR - http://eudml.org/doc/15266
ER -

References

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  8. N. I. Ioakimidis, General Methods for the Solution of Crack Problems in the Theory of Plane Elasticity, Doctoral Thesis at the National Technical University of Athens, Athens, 1976. [Available from University Microfilms, Ann Arbor, Michigan; Order No. 76-21, 056.] (1976) Zbl0351.73109MR0521392
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  14. D. G. Sanikidze, On a Uniform Estimation of Approximation of Singular Integrals with Chebyshev's Weight Function by Sums of Interpolating Type, Soobščenija Akademii Nauk Gruzinskoī SSR, 1974, Vol. 75 (No. 1), pp. 53-55 (in Russian). (1974) MR0358242
  15. M. A. Sheshko, On the Convergence of Quadrature Processes for a Singular Integral, Soviet Mathematics (Izvestija Vysših Učebnyh Zavedeniī. Matematika), 1976, Vol. 20 (No. 12), pp. 86-94. (1976) 
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