Approximate Methods for Calculating Singular and Hypersingular Integrals with Rapidly Oscillating Kernels

Abstract

The article is devoted to the issue of construction of an optimal with respect to order passive algorithms for evaluating Cauchy and Hilbert singular and hypersingular integrals with oscillating kernels. We propose a method for estimating lower bound errors of quadrature formulas for singular and hypersingular integral evaluation. Quadrature formulas were constructed for implementation of the obtained estimates. We constructed quadrature formulas and estimated the errors for hypersingular integrals with oscillating kernels. This method is based on using similar results obtained for singular integrals.

Keywords

• singular integrals
• hypersingular integrals
• optimal quadrature formulas
• oscillating kernels
• error estimation