The cubature formula of degree 4 for triangle, tetrahedron and 4-simplex

• Autorzy: Stańdo J.
• Języki publikacji: EN

Abstrakty

EN

Assume that the domain D is multidil1lensional region of integration given by unions of simplices T. Consider [wzór], are approximated by finite sums of the form [wzór], where WiT are weighs and xiT ∈ T are nodes. I present new cubature schemes for triangle, tetrahedron and 4-simplex exact for polynomials of fourth degree and the algorithm computing the integral and control error procedure. Software for the polygon is in the Appendix. Subject Classification AMS 65D32.

Słowa kluczowe

EN

cubature formula; cubature scheme; numerical cubature; triangle; tetrahedron; 4-symplex; numerical modelling

PL

trójkąt; czworościan; 4-sympleks; modelowanie numeryczne

• Wydawca: Wydawnictwo Politechniki Łódzkiej
• Czasopismo: Journal of Applied Computer Science
• Rocznik: 2003
• Tom: Vol. 11, nr 1
• Strony: 77--89
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Stańdo J.

• Institute of Mathematics, Technical University of Łódź, Al. Politechniki 11, 90-924 Łódź, Poland,

Bibliografia

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• [2] Laurie D.: CUBTRI Automatic cubature over a triangle, ACM Math. Software *, 1982,210-218.
• [3] Cools R. and Haegemans A.: An embedded pair of cubature formulae of degree 5 and 7 for the triangle, 1988 KUL, Belgium.
• [4] Lyness J.N. and Jespersen D.: Moderate degree symmetric quadrature rules for the triangle, J. INST. Maths Applies. (1975) 15, 19-32.
• [5] Schmid H.J.: Cubature formulas with a minimal number of knots, Numer. Math. 31 (281-297) 1978.
• [6] Stroud A.H.: Some approximate integration formulas of degree 3 for simplices, Math. Comp. 18 (1964) 590-597.
• [7] Lyness J.N., Cools R.: A Survey of numerical cubature over triangles, Applied Math, Vol. 48, 1994.
• [8] Berntsen J., Cools R., Espelid T.O.: Algorithm 720.An algorithm for adaptive cubature over a collection of 3-dimensional simplices, ACM Transaction on Mathematical, Vol. 19, No.3, September 1993.