Product of Turán quadratures for cube, simplex, surface of the sphere, Enr, Enr2
✍ Scribed by Miodrag M. Spalević
- Book ID
- 104338928
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 135 KB
- Volume
- 106
- Category
- Article
- ISSN
- 0377-0427
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✦ Synopsis
In this paper we give a method for construction of cubature formulas, for approximate calculations of multiple integral over regions: the cube, the simplex, surface of the sphere, E r n and E r 2 n , by using combinations, or products, of the generalized Turà an quadratures. The case s = 0 is given in Mysovskih (Interpolating Cubature Formulas, FM Moskva, 1981 (in Russian)) and Stroud (Approximate Calculation of Multiple Integrals, Prentice-Hall, Englewood Cli s, NJ, 1971). We give the generalized case, s ∈ N ∪{0}, where values of the integrand and its partial derivatives in the nodes are given. This method is based on the results from Milovanovià c (in: G.V. Milavanovià c (Ed.), Numerical Methods and Approximation