Advanced search
Publication Cover
Australian Journal of Mechanical Engineering Volume 11, 2013 - Issue 1: Meshless and Boundary Element Methods
Submit an article Journal homepage
10
Views
0
CrossRef citations to date
0
Altmetric
technical paper

The extrapolation methods for computing Cauchy principal value integral on intervals

J LiSchool of Science, Shandong Jianzhu University, Jinan, ChinaCorrespondence[email protected]
View further author information
Pages 61-65 | Published online: 16 Nov 2015

References

  • Amari, S. 1994, “Evaluation of Cauchy principal-value integrals using modified Simpson rules”, Appl. Math. Lett., Vol. 7, pp. 19–23.
  • Criscuolo, G. & Mastroianni, G. 1989, “On the Uniform Convergence of Gaussian Quadrature Rules for Cauchy Principal Value Integrals”, Numer. Math., Vol. 54, pp. 445–461.
  • Diethelm, K. 1995a, “Gaussian quadrature formulae of the third kind for Cauchy principal value integrals: basic properties and error estimates”, J. Comput. Appl. Math., Vol. 65, pp. 97–114.
  • Diethdm, K. 1995b, “Asymptotically Sharp Error Bounds for a Quadrature Rule for Cauchy Principal Value Integrals Based on Piecewise Linear Interpolation”, Approx. Theory and its Appl., Vol. 11, pp. 78–89.
  • Kim, P. & Choi, U. J. 2000, “A quadrature rule of interpolatory type for Cauchy integrals”, J. Comput. Appl. Math., Vol. 126, pp. 207–220.
  • Kim. P. & Yun, B. I. 2002, “On the convergence of interpolatory-type quadrature rules for evaluating Cauchy integrals”, J. Comput. Appl. Math., Vol. 149, pp. 381–395.
  • Li, J. & Yu, D. H. 2011a, “The Superconvergence of Certain Two-Dimensional Cauchy Principal Value Integrals”, CMES, Vol. 71, No. 4, pp. 331–346.
  • Li, J. & Yu, D. H. 2011b, “The superconvergence of certain two-dimensional Hilbert singular integrals”, CMES, Vol. 82, No. 4, pp. 233-252
  • Li, J., Wu, J. M. & Yu, D. H. 2009, “Generalized extrapolation for computation of hypersingular integrals in boundary element methods”, CMES, Vol. 42, pp. 151–175.
  • Li, J., Zhang, X. P. & Yu, D. H. 2010 “Superconvergence and ultraconvergence of Newton-Cotes rules for supersingular integrals”, J. Comput. Appl. Math., Vol. 233, pp. 2841–2854.
  • Liu, D. J., Wu, J. M. & Yu, D. H. 2010, “The superconvergence of the Newton-Cotes rule for Cauchy principal value integrals”, J. Comput. Appl. Math., Vol. 235, pp. 696–707.
  • Yu, D. H. 2002, Natural Boundary Integrals Method and its Applications, Kluwer Academic Publishers.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.