TY - JOUR
T1 - Numerical Integration Formulas for Hypersingular Integrals
AU - Shadimetov , Kholmat M.
AU - Akhmedov , Dilshod M.
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 3
SP - 805
EP - 826
PY - 2024
DA - 2024/08
SN - 17
DO - http://doi.org/10.4208/nmtma.OA-2024-0028
UR - https://global-sci.org/intro/article_detail/nmtma/23375.html
KW - Optimal quadrature formula, extremal function, Sobolev space, optimal coefficients, Hadamard type singular integral.
AB - <p style="text-align: justify;">It is known that the solution of the Cauchy problem for partial differential equations of hyperbolic type can be reduced to singular integrals of a unique
form. Laterly, singular integrals were called integrals in the sense of Hadamard or
Hadamard integrals. In addition to equations of the hyperbolic type, Hadamard integrals are widely used in elasticity, electrodynamics, aerodynamics, and other vital
areas of mechanics and mathematical physics. The exact evaluation of Hadamard
integrals is possible only in exceptional cases, so that there is a need to develop
approximate methods for their evaluation. In the present paper, we develop an optimal algorithm for the approximate calculation of Hadamard integrals. Here, we
deal with finding the analytical form of the coefficients of an optimal quadrature
formula. Numerical results show the validity and accuracy of the method.</p>