About the optimal cubature formulas in the anisotropic Sobolev spaces

The article based on the functional-analytical method of the theory of cubature formulas gives an overview of the functional errors and extreme functions. The elementary functionality of an error constructed on the plane with the knots lying inside or on border of any smooth area considers properties of the space interfaced to the anisotropic. To construct the optimal coefficients of the formulas the requirements of coherence are fulfilled. The effective algorithm is developed for calculation of optimum coefficients of values of function and its derivatives. It allowed on elementary error functionals replace some other lattice sites to be reduced to the minimum of the rate-of functionality and, thus, improve the quality of the formula. In these formulas the coefficients considering the differential nature of subintegral function were defined. With application of methods of computer algebra the algorithm of calculation of integrals has been improved. The calculated coefficients improve qualities of the cubature formulas in anisotropic spaces of Sobolev. The results of the received methods are tested on control tasks with known solutions.