Abstract
A quadrature formula has been constructed for calculating the hypersingular integral over a segment, which uses the ends of the segment partition intervals as nodes of piecewise constant interpolation of the integral density, as well as specially selected collocation points. A distinctive feature of the proposed quadrature formula is the ability to calculate the integral of functions that suffer a finite number of discontinuities of the first kind on the integration interval. On the basis of quadrature formula constructed, a numerical scheme for solving the characteristic hypersingular integral equation on non-regular grid is developed. Estimate of the rate of convergence of approximate solutions to exact ones is proved in the class of piecewise Ho¨lder functions.
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