OPTIMAL METHODS OF MULTIDIMENSIONAL HYPER SINGULAR INTEGRAL EVALUATION

Boykov Ilya Vladimirovich, Doctor of physical and mathematical sciences, professor, head of sub-department of higher and applied mathematics, Penza State University, math@pnzgu.ru
Zakharova Yuliya Fridrikhovna, Candidate of physical and mathematical sciences, associate professor, sub-department of higher and applied mathematics, Penza State University, math@pnzgu.ru

517.392

The authors suggest a method of lower estimate of calculation error of mul-tidimensional hypersingular integrals by cubature formulas, applying N nodes of a subintegral function. The estimations has been obtained for arbitrary class of the function ψ , integrated in the sense of Hadamard. For the range of function classes the authors have built cubatury formulas, optimal in order and accuracy.

multidimensional hypersingular integrals, cubatury formulas, accuracy-optimal algorithms.