An Optimal Method for the Approximate Solution of the Hypersingular Integral Equations

Hypersingular integral equations are encountered in a number of fields, such as the dynamics of air and fluid flow, elasticity, and wave propagation theory. Analytical solutions for these integral equations exist, but the solutions themselves are also expressed through singular integrals. Therefore, it becomes necessary to develop formulas for the approximate calculation of these solutions, and such formulas have been developed. Among these formulas, very few are highly accurate. However, they are not optimal. Our work is devoted to constructing an optimal quadrature formula for the approximate calculation of the analytical solutions of a hypersingular integral equation.