Product of Turلn quadratures for cube, simplex, surface of the sphere, Enr, Enr2

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, Enr and Enr2, by using combinations, or products, of the generalized Turán 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 Cliffs, 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 Milovanović (in: G.V. Milavanović (Ed.), Numerical Methods and Approximation Theory III, Univ. Nis, Nis, 1988, pp. 311–328), Milovanović and Spalević (Filomat (Nis) 9 (1) (1995) 1–8) and Spalevic (Zb. Rad. (Kragujevac) 17 (1995) 77–84). Numerical examples are included.