Construction of a Cubature Formula of the Fifth Degree of Accuracy Containing the Values of Partial Derivatives
Keywords:
cubature formula, degree of algebraic accuracyAbstract
A number of books by I.P. Mysovkikh, A.H. Stroud, V.I. Krylov and H.T. Shulgina are devoted to the approximate calculation of integrals, where the theory of constructing quadrature and cubature formulas is presented and exact formulas for algebraic polynomials of degree ???? for standard domains such as ???? – dimensional cube, ???? – dimensional ball, surface of ???? – dimensional ball (sphere), ???? – dimensional space with weight functions, where are given. In the works by Y.Xu, G.P. Ismatullayev, S.A. Bakhramov, cubature formulas were constructed using orthogonal polynomials by the reproducing kernel method and the Radon method with the minimum number of nodes for the domain and the weight where without the participation of partial derivatives. In this paper, we construct a cubature formula for the domain Ω and the weight exact for polynomials of the fifth degree involving the values partial derivatives at the point (0, 0).
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Copyright (c) 2024 Г.П. Исматуллаев, С.А. Бахромов, Р.Н. Мирзакабилов (Автор)
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