Home – Home – Jornals – Numerical Analysis and Applications 2022 number 3

This paper is devoted to constructing quadrature formulas for singular and hypersingular integrals evaluation. For evaluating the integrals with the weights (1- t )^γ₁(1+ t )^γ₂, γ₁, γ₂ > -1, defined on [-1,1], we have constructed quadrature formulas uniformly converging on [-1,1] to the original integral with the weights (1- t )^γ₁(1+ t )^γ₂, γ₁, γ₂ ≥ -1/2, and converging to the original integral for -1< t <1 with the weights (1- t )^γ₁(1+ t )^γ₂, γ₁, γ₂ > -1. In the latter case a sequence of quadrature formulas converges to evaluating integral uniformly on [-1+δ,1-δ], where δ > 0 is arbitrarily small. We propose a method for construction and error estimate of quadrature formulas for evaluating hypersingular integrals based on transformation of quadrature formulas for evaluation of singular integrals. We also propose a method of the error estimate for quadrature formulas for singular integrals evaluation based on the approximation theory methods. The results obtained were extended to hypersigular integrals.