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.
This work was supported by the Applied Mathematical Sciences Research Program (KC-04–02) of the Office of Energy Research of the U.S. Department of Energy under Contract W-31–109-Eng-38.
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References
Lyness, J. N. and Gatteschi, L. 1982. On Quasi Degree Quadrature Rules. Submitted to Num. Math.
Lyness, J. N. and Jespersen, D. 1975. Moderate Degree Symmetric Quadrature Rules for the Triangle. J. Inst. Maths Applics 15, 19–32.
Stroud, A. H. 1971. Approximate Calculation of Multiple Integrals. Englewood Cliffs, N.J., Prentice Hall, Inc.
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Lyness, J.N., Gatteschi, L. (1982). A Note on Cubature over a Triangle of a Function Having Specified Singularities. In: Hämmerlin, G. (eds) Numerical Integration. ISNM 57: International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 57. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6308-7_16
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DOI: https://doi.org/10.1007/978-3-0348-6308-7_16
Publisher Name: Birkhäuser, Basel
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