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A Note on Cubature over a Triangle of a Function Having Specified Singularities

  • J. N. Lyness
  • L. Gatteschi
Chapter
Part of the ISNM 57: International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique book series (ISNM, volume 57)

Abstract

The conical product rules for integration over a triangle ABC are well known. In this note, we discuss conical product rules with weight function w(x)rß where r is the distance of (x,y) from C and x is the distance of (x,y) from AB. In particular we show how to construct rules which are exact for integrand functions pλ(x,y)hμ(r) where pλ and hμ are polynomials of degree λ and μ, respectively.

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References

  1. Lyness, J. N. and Gatteschi, L. 1982. On Quasi Degree Quadrature Rules. Submitted to Num. Math.Google Scholar
  2. Lyness, J. N. and Jespersen, D. 1975. Moderate Degree Symmetric Quadrature Rules for the Triangle. J. Inst. Maths Applics 15, 19–32.CrossRefGoogle Scholar
  3. Stroud, A. H. 1971. Approximate Calculation of Multiple Integrals. Englewood Cliffs, N.J., Prentice Hall, Inc.Google Scholar

Copyright information

© Springer Basel AG 1982

Authors and Affiliations

  • J. N. Lyness
  • L. Gatteschi

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