Skip to main content
SpringerLink
Log in

Symmetric quadrature formulas over a unit disk

  • Published:
Korean Journal of Computational & Applied Mathematics Aims and scope Submit manuscript

Abstract

An algorithm to get an optimal choice for the number of symmetric quadrature points is given to find symmetric quadrature formulas over a unit disk with a minimal number of points even when a high degree of polynomial precision is required. The symmetric quadrature formulas for numerical integration over a unit disk of complete polynomial functions up to degree 19 are presented.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. D.A.Dunavant,Economical symmetrical quadrature rules for complete polynomials over a square domain, Int.J.Numer.Methods eng.21 (1985), 1777–1784.

    Article  MathSciNet  Google Scholar 

  2. K.Gatermann,The Construction of symmetric cubature formulas for the square and the triangle, Computing40 (1988), 229–240.

    Article  MathSciNet  Google Scholar 

  3. P.C.Hammer, O.J.Marlowe and A.H.Stroud,Numerical integration over simplexes and cones, MTAC10 (1956), 130–137.

    MathSciNet  Google Scholar 

  4. P.C.Hammer and A.H.Stroud,Numerical evaluation of multiple integrals II, MTAC12 (1958), 272–280.

    MathSciNet  Google Scholar 

  5. International Mathematical and Statistical Libraries,version 2.0, Visual Numerics Inc., Houston,Texas, 1991.

  6. M.E.Laursen and M.Gellert,Some criteria for numerically integrated matrices and quadrature formulas for triangles, Int. J.Numer.Methods Eng.12 (1978), 67–76.

    Article  Google Scholar 

  7. J.N.Lyness and D.Jespersen,Moderate degree symmetric quadrature rules for the triangle, Inst.Maths.Applies.15 (1975), 19–32.

    Article  MathSciNet  Google Scholar 

  8. Mathematica,enhanced version 2.2, Wolfram Research,Inc., 1993.

  9. Microsoft Fortran Powerstation,Professional Edition, version 4.0, Microsoft Corporation, 1995.

  10. P.Rabinowitz and N.Richter,Perfectly symmetric two dimensional integration formulas with minimal number of points, Math. Comp.23 (1969), 765–779.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Yonsei University, 120-749, Seoul, Korea

    KyoungJoong Kim

  2. Department of Computer Sciences, Yonsei University, 120-749, Seoul, Korea

    ManSuk Song

Authors
  1. KyoungJoong Kim
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. ManSuk Song
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to KyoungJoong Kim.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kim, K., Song, M. Symmetric quadrature formulas over a unit disk. Korean J. Comp. & Appl. Math. 4, 179–192 (1997). https://doi.org/10.1007/BF03011388

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03011388

AMS Mathematics Subject Classification

Key words and phrases

Search

Navigation